{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Chapter 4 – Training Linear Models**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_This notebook contains all the sample code and solutions to the exercises in chapter 4._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's make sure this notebook works well in both python 2 and 3, import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# To support both python 2 and python 3\n",
    "from __future__ import division, print_function, unicode_literals\n",
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "np.random.seed(42)\n",
    "\n",
    "# To plot pretty figures\n",
    "%matplotlib inline\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "mpl.rc('axes', labelsize=14)\n",
    "mpl.rc('xtick', labelsize=12)\n",
    "mpl.rc('ytick', labelsize=12)\n",
    "\n",
    "# Where to save the figures\n",
    "PROJECT_ROOT_DIR = \".\"\n",
    "CHAPTER_ID = \"training_linear_models\"\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True):\n",
    "    path = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID, fig_id + \".png\")\n",
    "    print(\"Saving figure\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format='png', dpi=300)\n",
    "\n",
    "# Ignore useless warnings (see SciPy issue #5998)\n",
    "import warnings\n",
    "warnings.filterwarnings(action=\"ignore\", message=\"^internal gelsd\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear regression using the Normal Equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "X = 2 * np.random.rand(100, 1)\n",
    "y = 4 + 3 * X + np.random.randn(100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure generated_data_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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R9r82Wlld7PbWytB0QG0BjgRuBx4GPgX8RlMrn/TRd5Nf9GEVWVMBPBgQw9bbZoiUWuGOsv813covsdtRmtNoQGXmo8Bbej+tqKviHKwEm/6iD6vI3vOedrq/Sup2K73CXWz/a7qVP+3d3uo278W3BMMqwaa/6PNVZG0+ZK+Eiq3rFW7TYT9t3d6aLlMXUE107wyrBJv+opfUailJE/8Pk97Hmgx79yOVLDIbHUg3tpmZmZydnR1p3qa6d+Zbz1IqrlLPlwzqSjlhsmUtvQtRalNE3JKZM3Utb6paUE1178x31Dnuke+oQdd2OHStUp5kC6TrXYhSl0xVQDXZzVZHJTissoMnX1N0/vnthsNSKuW2Q3VSPGcjNWeqAqrk/vRhFfawym4wDD796faP2MetlLvW4hpHyfuYNG06HVDDKv1Sbgk0uK5hFfZ8lV1/GJx+Otx4Y7tH7ONWytPeDVbKiEVp2nU2oJZzlF7CNUvzBeqwMDj++PaP2MeplCfxIMG2P7+k5nU2oJZzlF7KNUvzGRZa85WvxMq7P2SPOGJ5d++e5u5CSQvrbEAt5yh9Wq5ZKrnynivHKI/mKOnWP5LK0dmAWk6lP+xv27r4cjnrLb3yXqx8owSso+aklauzAQWjnReZLwDm/r19O9x6K7z1rfDoo7BmzfIq+nECZ7ktoNIr78XKN0rAOmpOWrk6HVCLWSgA+qdBVUlC9fqaa5o5X7LcFlDplfdi5Rs1YB01J61MnQiopXaDLRQA/dMi6innuIFTRwuo9Mp7ofKVHrCS2lV8QD344NK7wRYKgP5pq1ZBJjz2WPXeWWctraxLGa230ivo0gNWUnuKv1nss541kzt3zrJvXxUkW7ZUzz2as1jraqHp/dOgnqAocdi3JDWh7pvFFh9Qxx47k3ffPbvoeaTShllL0kpTd0AdUNeCJuXgg6vg2bLlyQE0381W1awdO2Dr1uq3JNWl+HNQMP95itKHWa8EtmIlTUonAmo+DjJoX+kXC0vqrlYCKiJ+HLgV+IPMfN1yluUosHbZipU0KW21oD4KfKWlddduJY/csxUraVIaD6iIOAP4HvAl4MeaXn/dPAdjK1bSZDQ6ii8iDgPeB7xjkfk2RcRsRMzu2rWrmcItUZsjCR09J2maNd2C2gJcnpnfiQXuL5SZ24BtADMzM0VfqNXWORhbbpKmXWMBFREnAKcCL2pqnU1o6xyMo+ckTbsmW1AbgQ3At3utp0OAVRHx/Mz8yQbLUbs2zsE4ek7StGsyoLYBn+x7/atUgfXmBsswNRw9J2naNRZQmfkD4AdzryNiD/BwZpY9CqJgjp6TNM1au5NEZm5ua92jWsnXN0lS2zp9q6NRLDVkHCUnSe2a6oBaTsg4Sk6S2lX84zaWYzkX0c6Nklu1qp5Rcl5UK0njmeoW1HKGYtc5Ss7uQkka31QH1HJDpq5RcnYXStL4pjqgoIyh2F5UK0njm/qAKoEX1UrS+AyohpTQkpOkLpnqUXySpO4yoCRJRTKgJElFMqAkSUUyoCRJRTKgJElFMqAkSUUyoCRJRTKgJElFMqAkSUUyoCRJRWosoCLioIi4PCLujojdEfE3EXFaU+uXJHVLky2o1cD/BV4K/AhwAfCpiNjQYBkkSR3R2N3MM/NBYHPfW38cEXcC/wK4q6lySJK6obVzUBFxFHAMcNuQaZsiYjYiZnft2tV84SRJrWsloCJiDfAx4OrM/Obg9MzclpkzmTmzbt265gsoSWpd4wEVEQcA1wKPAOc2vX5JUjc0+kTdiAjgcuAo4Gcz89Em1y9J6o6mH/n+O8CxwKmZ+VDD65YkdUiT10EdDbwJOAHYGRF7ej9nNlUGSVJ3NDnM/G4gmlqfJKnbvNWRJKlIBpQkqUgGlCSpSAaUJKlIBpQkqUgGlCSpSAaUJKlIBpQkqUgGlCSpSAaUJKlIBpQkqUgGlCSpSAaUJKlIBpQkqUgGlCSpSAaUJKlIBpQkqUgGlCSpSAaUJKlIBpQkqUiNBlREHB4RfxgRD0bE3RHxy02uX5LUHasbXt9HgUeAo4ATgP8VEV/NzNsaLockqXCNtaAi4mDgdODCzNyTmX8J/BHw+qbKIEnqjiZbUMcAj2Xm7X3vfRV46eCMEbEJ2NR7uTcivt5A+ep2JHBv24UYUxfLDN0sdxfLDN0sdxfLDN0s93PrXFiTAXUI8MDAe98HDh2cMTO3AdsAImI2M2cmX7x6dbHcXSwzdLPcXSwzdLPcXSwzdLPcETFb5/KaHCSxBzhs4L3DgN0NlkGS1BFNBtTtwOqI+PG+934CcICEJOlJGguozHwQuA54X0QcHBEnAa8Erl3kT7dNvHCT0cVyd7HM0M1yd7HM0M1yd7HM0M1y11rmyMw6l7fwyiIOB64AXgbcB7w7Mz/eWAEkSZ3RaEBJkjQqb3UkSSqSASVJKlIrATXqPfmi8v6IuK/38/6IiL7pJ0TELRHxg97vEwoo8zsj4usRsTsi7oyIdw5MvysiHoqIPb2fP51Umccs9+aIeLSvXHsi4tl900vc1jcMlPeRiLi1b3pj2zoizo2I2YjYGxFXLTLv2yNiZ0Q8EBFXRMRBfdM2RMRf9LbzNyPi1EmVeZxyR8TZvf/3ByLiOxHxgYhY3Td9e0Q83Letv1VAmc+JiH0D+8jGvumlbuvLBsq8NyJ2901vclsfFBGX976HuyPibyLitAXmr3ffzszGf4BPAL9HdfHuT1FdsHvckPneBHwLeBbwTOAbwK/0ph0I3A28HTgIOK/3+sCWy/xrwE9SXQT93F6ZzuibfhdwaoHbejPwu/Mso8htPeTvtgMXtbGtgVcDrwJ+B7hqgfleDvwjcBzwtF6Z/1Pf9B3Ah4CnUN0a7HvAugLK/Wbg5N6+8EzgFqpBTv3b/o2FbetzgL9cYHqR23rI310FXNHStj64VzdsoGrQ/DzVtasbhsxb+7498Q84zwd+BDim771r+z9I3/tfAjb1vf53wM29f/8M8Pf0Bnr03vs28Io2yzzkb38L+O2+101WmuNs683MH1DFb+veF2hf/xenyW3dt85LFqk0Pw78Zt/rU4CdvX8fA+wFDu2bfiO9g7I2yz1k/ncAn+l73VilOca2Pod5Aqor27r3fdgNvLTNbT1Qpq8Bpw95v/Z9u40uvvnuyXfckHmP600bNt9xwNey90l7vjbPcpZrnDL/UEQE1VHn4MXIH4uIXRHxpxHxE/UWdT/jlvsXIuK7EXFbRLy57/3itzVwFnBjZt418H5T23pUw/bpoyLiiN60OzJz98D0SWzn5XoJT96vt0bEvRFxU39XWste1CvT7RFxYV+3ZFe29enALuCLA++3sq0j4iiq7+iwGyzUvm+3EVAj35OvN+/3B+Y7pFfxD05baDnLNU6Z+22m2sZX9r13JtXR/tHAXwB/EhFPraWUTzZOuT8FHAusA/49cFFEvLZvOaVv67OoukL6NbmtRzVsn4bq8zW5nZcsIt4AzAAf7Hv7XcCzqbr/tgGfiYjntFC8fl8EXgA8naqify0wd064E9saOBu4ZuDgsJVtHRFrgI8BV2fmN4fMUvu+3UZAjXNPvsF5DwP29P6zmry339jriohzqSrNn8vMvXPvZ+ZNmflQZv4gM7dS9cOePIEywxjlzsxvZOY9mbkvM78E/BfgF8ddTg2Wsq1/CvinwB/0v9/wth7VsH0aqs9X/P0qI+JVwFbgtMz84Z22M/OvMnN3Zu7NzKuBm4CfbaucvTLdkZl3ZubjmXkr8D7a2aeXJCLWAxuBa/rfb2NbR8QBVF3tjwDnzjNb7ft2GwE1zj35butNGzbfbcALe62pOS+cZznLNdZ9BHtHmO8GTsnM7yyy7ARikXmWajn3P+wvV7Hbuuds4LrM3LPIsie5rUc1bJ/+x8y8rzft2RFx6MD0Iu5XGRGvAP478Au9Cn8hJWzrQYP7dLHbuuf1wE2Zecci8010W/e+95dTPWj29Mx8dJ5Z69+3WzrJ9kmqkVoHAycx/8iyXwH+lqop+896H2ZwFN/bqEaWnctkR5aNWuYzgZ3AsUOmre/97YHAWqruhl3AEQVs61dSjbwJ4MVUgyLOLnlb9+Z9Sm/6T7e5ralGba6lal1c2/v36iHzvaK3fzwfeCrwBfYf6XQzVdfZWuDfMPmRZaOW+6epbk/2kiHTnko1gmttb3lnAg/SN9ClpTKfBhzV+/fzgK8DF5e+rfvm/xbwhja3dW+dl/W21SGLzFf7vj2RDzTCBz4cuL63Yb8N/HLv/ZOpuvDm5gvgA8B3ez8fYP+RZC+iGu76EPDXwIsKKPOdwKNUTdq5n8t6046jGlzwYO/L/nlgppBt/YlemfYA3wTOG1hOcdu6995rqcIyBt5vdFtTnW/MgZ/NVEG5B1jfN+87qIbjPkB1fvKgvmkbqEZpPURVQU10FOKo5aY6h/fYwH59Q2/aOuArVN0136OqiF5WQJk/2NvODwJ3UHXxrSl9W/fmPbFX7kMHltH0tj66V86HB/7vz2xi3/ZefJKkInmrI0lSkQwoSVKRDChJUpEMKElSkQwoSVKRDChJUpEMKElSkQwoSVKRDChJUpEMKGkCIuIpvUejf7v/sde9af+j9yjyM9oqn9QFBpQ0AZn5EHAx8KPAW+bej4itVE+GfmtmfrKl4kmd4L34pAmJiFVUTw19OtUD5t4IfJjqjtrva7NsUhcYUNIERcTPA5+hevTAvwYuzczz2i2V1A0GlDRhEfHXVI8r+STVo0NyYPq/Bc4DTgDuzcwNjRdSKpDnoKQJiohf4omnjO4eDKee+4FLgV9vrGBSB9iCkiYkIn6GqnvvM1QPsXwNcHxm/u08878K+IgtKKliC0qagIj4l8B1wE1UTx+9AHic6nHfkkZgQEk1i4jnA58FbgdelZl7M/PvgMuBV0bESa0WUOoIA0qqUUSsB/6E6rzSaZn5QN/kLcBDwAfaKJvUNavbLoA0TTLz21QX5w6bdg/wT5otkdRdBpTUst4FvWt6PxERa4HMzL3tlkxqlwElte/1wJV9rx8C7gY2tFIaqRAOM5ckFclBEpKkIhlQkqQiGVCSpCIZUJKkIhlQkqQiGVCSpCIZUJKkIv1/zuSC65hhRY0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "save_fig(\"generated_data_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_b = np.c_[np.ones((100, 1)), X]  # add x0 = 1 to each instance\n",
    "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new = np.array([[0], [2]])\n",
    "X_new_b = np.c_[np.ones((2, 1)), X_new]  # add x0 = 1 to each instance\n",
    "y_predict = X_new_b.dot(theta_best)\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_predict, \"r-\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.axis([0, 2, 0, 15])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure in the book actually corresponds to the following code, with a legend and axis labels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure linear_model_predictions\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_predict, \"r-\", linewidth=2, label=\"Predictions\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "save_fig(\"linear_model_predictions\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.21509616]), array([[2.77011339]]))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.predict(X_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `LinearRegression` class is based on the `scipy.linalg.lstsq()` function (the name stands for \"least squares\"), which you could call directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best_svd, residuals, rank, s = np.linalg.lstsq(X_b, y, rcond=1e-6)\n",
    "theta_best_svd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function computes $\\mathbf{X}^+\\mathbf{y}$, where $\\mathbf{X}^{+}$ is the _pseudoinverse_ of $\\mathbf{X}$ (specifically the Moore-Penrose inverse). You can use `np.linalg.pinv()` to compute the pseudoinverse directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.pinv(X_b).dot(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: the first releases of the book implied that the `LinearRegression` class was based on the Normal Equation. This was an error, my apologies: as explained above, it is based on the pseudoinverse, which ultimately relies on the SVD matrix decomposition of $\\mathbf{X}$ (see chapter 8 for details about the SVD decomposition). Its time complexity is $O(n^2)$ and it works even when $m < n$ or when some features are linear combinations of other features (in these cases, $\\mathbf{X}^T \\mathbf{X}$ is not invertible so the Normal Equation fails), see [issue #184](https://github.com/ageron/handson-ml/issues/184) for more details. However, this does not change the rest of the description of the `LinearRegression` class, in particular, it is based on an analytical solution, it does not scale well with the number of features, it scales linearly with the number of instances, all the data must fit in memory, it does not require feature scaling and the order of the instances in the training set does not matter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear regression using batch gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "eta = 0.1\n",
    "n_iterations = 1000\n",
    "m = 100\n",
    "theta = np.random.randn(2,1)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n",
    "    theta = theta - eta * gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new_b.dot(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_bgd = []\n",
    "\n",
    "def plot_gradient_descent(theta, eta, theta_path=None):\n",
    "    m = len(X_b)\n",
    "    plt.plot(X, y, \"b.\")\n",
    "    n_iterations = 1000\n",
    "    for iteration in range(n_iterations):\n",
    "        if iteration < 10:\n",
    "            y_predict = X_new_b.dot(theta)\n",
    "            style = \"b-\" if iteration > 0 else \"r--\"\n",
    "            plt.plot(X_new, y_predict, style)\n",
    "        gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n",
    "        theta = theta - eta * gradients\n",
    "        if theta_path is not None:\n",
    "            theta_path.append(theta)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    plt.axis([0, 2, 0, 15])\n",
    "    plt.title(r\"$\\eta = {}$\".format(eta), fontsize=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure gradient_descent_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.subplot(131); plot_gradient_descent(theta, eta=0.02)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(132); plot_gradient_descent(theta, eta=0.1, theta_path=theta_path_bgd)\n",
    "plt.subplot(133); plot_gradient_descent(theta, eta=0.5)\n",
    "\n",
    "save_fig(\"gradient_descent_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stochastic Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_sgd = []\n",
    "m = len(X_b)\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure sgd_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_epochs = 50\n",
    "t0, t1 = 5, 50  # learning schedule hyperparameters\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    for i in range(m):\n",
    "        if epoch == 0 and i < 20:                    # not shown in the book\n",
    "            y_predict = X_new_b.dot(theta)           # not shown\n",
    "            style = \"b-\" if i > 0 else \"r--\"         # not shown\n",
    "            plt.plot(X_new, y_predict, style)        # not shown\n",
    "        random_index = np.random.randint(m)\n",
    "        xi = X_b[random_index:random_index+1]\n",
    "        yi = y[random_index:random_index+1]\n",
    "        gradients = 2 * xi.T.dot(xi.dot(theta) - yi)\n",
    "        eta = learning_schedule(epoch * m + i)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_sgd.append(theta)                 # not shown\n",
    "\n",
    "plt.plot(X, y, \"b.\")                                 # not shown\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)                     # not shown\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)           # not shown\n",
    "plt.axis([0, 2, 0, 15])                              # not shown\n",
    "save_fig(\"sgd_plot\")                                 # not shown\n",
    "plt.show()                                           # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21076011],\n",
       "       [2.74856079]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SGDRegressor(alpha=0.0001, average=False, early_stopping=False, epsilon=0.1,\n",
       "       eta0=0.1, fit_intercept=True, l1_ratio=0.15,\n",
       "       learning_rate='invscaling', loss='squared_loss', max_iter=50,\n",
       "       n_iter=None, n_iter_no_change=5, penalty=None, power_t=0.25,\n",
       "       random_state=42, shuffle=True, tol=-inf, validation_fraction=0.1,\n",
       "       verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDRegressor\n",
    "sgd_reg = SGDRegressor(max_iter=50, tol=-np.infty, penalty=None, eta0=0.1, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.16782089]), array([2.72603052]))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg.intercept_, sgd_reg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mini-batch gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_mgd = []\n",
    "\n",
    "n_iterations = 50\n",
    "minibatch_size = 20\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "t0, t1 = 200, 1000\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "t = 0\n",
    "for epoch in range(n_iterations):\n",
    "    shuffled_indices = np.random.permutation(m)\n",
    "    X_b_shuffled = X_b[shuffled_indices]\n",
    "    y_shuffled = y[shuffled_indices]\n",
    "    for i in range(0, m, minibatch_size):\n",
    "        t += 1\n",
    "        xi = X_b_shuffled[i:i+minibatch_size]\n",
    "        yi = y_shuffled[i:i+minibatch_size]\n",
    "        gradients = 2/minibatch_size * xi.T.dot(xi.dot(theta) - yi)\n",
    "        eta = learning_schedule(t)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_mgd.append(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.25214635],\n",
       "       [2.7896408 ]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_bgd = np.array(theta_path_bgd)\n",
    "theta_path_sgd = np.array(theta_path_sgd)\n",
    "theta_path_mgd = np.array(theta_path_mgd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure gradient_descent_paths_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7,4))\n",
    "plt.plot(theta_path_sgd[:, 0], theta_path_sgd[:, 1], \"r-s\", linewidth=1, label=\"Stochastic\")\n",
    "plt.plot(theta_path_mgd[:, 0], theta_path_mgd[:, 1], \"g-+\", linewidth=2, label=\"Mini-batch\")\n",
    "plt.plot(theta_path_bgd[:, 0], theta_path_bgd[:, 1], \"b-o\", linewidth=3, label=\"Batch\")\n",
    "plt.legend(loc=\"upper left\", fontsize=16)\n",
    "plt.xlabel(r\"$\\theta_0$\", fontsize=20)\n",
    "plt.ylabel(r\"$\\theta_1$   \", fontsize=20, rotation=0)\n",
    "plt.axis([2.5, 4.5, 2.3, 3.9])\n",
    "save_fig(\"gradient_descent_paths_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.random as rnd\n",
    "\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 0.5 * X**2 + X + 2 + np.random.randn(m, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure quadratic_data_plot\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"quadratic_data_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
    "X_poly = poly_features.fit_transform(X)\n",
    "X[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929,  0.56664654])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_poly[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.78134581]), array([[0.93366893, 0.56456263]]))"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X_poly, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure quadratic_predictions_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new=np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "X_new_poly = poly_features.transform(X_new)\n",
    "y_new = lin_reg.predict(X_new_poly)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"quadratic_predictions_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure high_degree_polynomials_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "for style, width, degree in ((\"g-\", 1, 300), (\"b--\", 2, 2), (\"r-+\", 2, 1)):\n",
    "    polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n",
    "    std_scaler = StandardScaler()\n",
    "    lin_reg = LinearRegression()\n",
    "    polynomial_regression = Pipeline([\n",
    "            (\"poly_features\", polybig_features),\n",
    "            (\"std_scaler\", std_scaler),\n",
    "            (\"lin_reg\", lin_reg),\n",
    "        ])\n",
    "    polynomial_regression.fit(X, y)\n",
    "    y_newbig = polynomial_regression.predict(X_new)\n",
    "    plt.plot(X_new, y_newbig, style, label=str(degree), linewidth=width)\n",
    "\n",
    "plt.plot(X, y, \"b.\", linewidth=3)\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"high_degree_polynomials_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "def plot_learning_curves(model, X, y):\n",
    "    X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=10)\n",
    "    train_errors, val_errors = [], []\n",
    "    for m in range(1, len(X_train)):\n",
    "        model.fit(X_train[:m], y_train[:m])\n",
    "        y_train_predict = model.predict(X_train[:m])\n",
    "        y_val_predict = model.predict(X_val)\n",
    "        train_errors.append(mean_squared_error(y_train[:m], y_train_predict))\n",
    "        val_errors.append(mean_squared_error(y_val, y_val_predict))\n",
    "\n",
    "    plt.plot(np.sqrt(train_errors), \"r-+\", linewidth=2, label=\"train\")\n",
    "    plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"val\")\n",
    "    plt.legend(loc=\"upper right\", fontsize=14)   # not shown in the book\n",
    "    plt.xlabel(\"Training set size\", fontsize=14) # not shown\n",
    "    plt.ylabel(\"RMSE\", fontsize=14)              # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure underfitting_learning_curves_plot\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "plot_learning_curves(lin_reg, X, y)\n",
    "plt.axis([0, 80, 0, 3])                         # not shown in the book\n",
    "save_fig(\"underfitting_learning_curves_plot\")   # not shown\n",
    "plt.show()                                      # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure learning_curves_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "polynomial_regression = Pipeline([\n",
    "        (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
    "        (\"lin_reg\", LinearRegression()),\n",
    "    ])\n",
    "\n",
    "plot_learning_curves(polynomial_regression, X, y)\n",
    "plt.axis([0, 80, 0, 3])           # not shown\n",
    "save_fig(\"learning_curves_plot\")  # not shown\n",
    "plt.show()                        # not shown"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regularized models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure ridge_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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gwLzVZfHx8axatYqoqCjuvvvuEvddFMXVYzfddBMXX3wxHTt2xOVyMWfOHObMmcPUqVM1vqc6ICJV6oiJiZGiiIuLK/K9qsScOXMkIiJCfH19pXPnzrJjxw6ZMWOGBAYGyqRJkxzvb+fOnQIUeuzcuTOvXmxsrPzpT38SPz8/ady4sTzxxBOSnZ3tmBzV5ftTPAHWSCXQHUUdZ9IpItXnvqyMemXv3r0ycOBAadKkifj5+cn5558vt99+u2zZssVxeXIpjh4bPXq0tG3bVvz9/cXPz086d+4s77333lnbri73SmXh2R+flQ/WfyBZriyP8tLqFCOliPuoCLp06SJr1qwp9L1NmzbRrl27cpZIcQr9/qonxpi1ItKlouUoijPpFND7Uik+eq84x9HUo4S9EEZQrSCOP3bcI7aqtDrFcZ+dMeYDY8xBY8xxY8wfxpgiI9GMMcONMYdO1X3XGFPbaXkURanaqE5RlJpH7JFYAKLCohwPKC+LycrngAgRCQauByYYYwpErhlj+gKPAb2AFkBL4KkykEdRlKqN6hRFqWHExlvDJzos2l04ejS8+26p23bc8BGRWBHJyH156mhVSNW7gXdO1U8CngHucVoeRVGqNqpTFKXmsfHIRgDaN2xvC44cgUmT4IHSr/Iqk/B0Y8zrxphUYDNwEFhQSLVoYH2+1+uBRsaYAssIjDGDjTFrjDFr4uPjy0JkRVEqMapTFKVmUcDj4+cHb7wBjz1W6rbLxPARkb8DdYArgHlARiHVgoD8KTRzn9cppL3pItJFRLqEhYU5La6iKJUc1SmKUnMQkbwYn+iGpwyf4GAYMgSeKv3sdZklJBARl4gsA5oDhfmmUoD8CWByn58oK5kURam6qE5RlJpBSmYKTeo0ISwgjGZ1nM3aDGVo+OTDh8Ln42OBC/O9vhA4LCIJ5SCToihVF9UpilKNqVO7Dhse2MDBEQftiq6ff4YXXoAdOxxp31HDxxjT0BhzqzEmyBjjfWqVxW3AkkKqvwfcZ4yJMsbUA54AZjgpj6IoVRvVKYpSc8nbkf3dd2HkSJg1y5F2nfb4CNYFvQ9IAl4E/iUinxtjwo0xKcaYcAARWQRMBr4H9gC7gXEOy6MoStVGdYqi1DBOZJzw3ENuwAC49Va46SZH2nd0ry4RiQcK3elNRPZggw/zl00Bpjgpg6Io1QfVKYpS8+g3qx+x8bF8c8c3dG3WFfr1s4dD6G5riqIoiqJUCkSE2PhYjqUfo3lw8zLpQw0fhW3btjFkyBA6duyIt7c3PXv2LLReXFwcvXr1IiAggKZNmzJ27FhcLleJ6ymKUn0prl5RlPwcTDnIsfRjhPiF0Lh2AxgzBlavBgf3FXV0qkupmsTGxrJgwQIuvfRSsrKyCq2TlJRE7969iYqKYv78+Wzfvp0RI0aQk5PDhAkTzrmeoijVm+LoFUU5nfz5e8z338Ozz8L//gexsY71oYaPQv/+/bnhhhsAGDBgAEePHi1Q58033yQtLY158+YRHBxMnz59OH78OOPHj2fkyJEEBwefUz1FUao3xdErinI6vx/+HYD2Ye2hRQt46CFo08bRPnSqq5KSmJjIkCFDCA0NpX79+owaNQqA7t27M23aNEf78vI6+22wcOFC+vbt62G43HrrraSlpfHDDz+ccz1FUcqfyqZXFOV01h1aB0DnJp0hMhKmTrXGj4Oox6cScuzYMS677DKCgoJ499132bhxI2PGjCEiIoLt27czaNAgj/oiUqwYGh+fkn/dmzdv5qqrrvIoCw8PJyAggM2bN9O/f/9zqqcoSvlSGfWKopzOuoP5DJ8yomaY5MbYIz/9+9uyL75wl02fbssGD3aXHThgy5o29Tw/JsaWr13rLhs/3paNH18qcSdOnMihQ4dYtGgR119/PY8//jihoaGMHj2aRx55BD8/P4/6M2fOxNfX96xHaUhKSqJevXoFykNCQkhKSjrneopS5VG9Umq9oiinM+OGGbza71UunPMDLFoE2dmO96GmeiVDRJg5cyaDBg0iNDQ0r7xu3bokJyczdOjQAuf079+f1atXl6eYigLAihWwdCn07AndulW0NEpRqF5RKjs5ORAfD5c0v4Sc2Ha88Ohkerqeptve9tDc2WXtNcPwKWwZXP4RWS6DB3uOysCOyAo7P/+ILJfx40s9KtuyZQvx8fH06dPHo9zlcjFs2DACAwMLnFO/fn3q1q1bqn7PRkhICMnJyQXKk5KSCAkJOed6StVnxQro1QsyM6FWLViypIYZP6pXFMUxPvwQ7roLGjaEhKN1kJynqeU9liV7a9HN4XQ+NWOqqwqxc+dOAFq0aJFXtnz5cnbt2kWnTp0KPac8XNKRkZFs3rzZo2zv3r2kpqYSGRl5zvWUqs/Spdbocbns49KlFS2RUhSVVa8oSi4ffggDp02hxVVfk+0Cl3iRSa0y0Ss1w+NThfD2tpuyJSYmAtZFPXLkyLznhVEeLul+/frxwgsvcOLECerUqQPAnDlz8Pf358orrzznekrVp2dP6+nJ9fhofrrKS2XVK4oCcPSo3YD9vGtnEBsQiJdPb8jxLjO9ooZPJSMmJgY/Pz9GjhzJmDFjmDNnDomJibRp04bZs2fToUMHIiIiPM5p0KABDRo0KHGfqampLFiwAID9+/dz/Phx5s6dC8A111xDQEAAQ4cOZerUqfzlL39h1KhR7Nixg/Hjx/Pwww97LF0vbj2lanJ6TM+SJRrjUxWorHpFUVasgMmT4aKuGSxLiOOexBw69vqSj4/2Y8q0WmWjV0SkSh0xMTFSFHFxcUW+V5WYM2eOREREiK+vr3Tu3Fl27NghM2bMkMDAQJk0aZLj/e3cuVOwu2AXOHbu3JlXLzY2Vv70pz+Jn5+fNG7cWJ544gnJzs4u0F5x651Odfn+qivLl4v4+4t4e9vH5cuLdx6wRiqB7ijqOJNOEak+92Vl1SvViepyr5QXuToFRHxrZYu591I5EOIrAvLABUuKPK+0OkU9PpWQW265hVtuucWj7Pzzz+fuu+8uk/4iIiKKdHfnJyoqiu+++86xekrVorCYHvXyVB0qq15Rai65OgXAlW0wu3qyYKDhrv3Nee/rnkzNhrJIE6XBzYqiFIvcmB5vb43pURSl9PTsCV5ep1Ji+WST03IpKXf8Fd/PPqZREy+2bi2bftXjoyhKsdCYHkVRnKRbN7jwQrszxcom97MtcCWdm0wGoFMnWL8e2rVzvl81fBRFKTbduqnBoyiKM7hc8Mcf8NVXwsIJu0n4oyEx958HWINo/Xq49Vbn+3V0qssYU9sY844xZrcx5oQx5jdjTL8i6t5jjHEZY1LyHT2dlEdRlKqN6hRFqb5s2mQTFjZskMPdX+zh4flHCPh9E2A9Pr/9Vjb9Ou3x8QH2AlcCe4BrgI+NMR1EZFch9VeISHcnBRARzOn751QAKSlw4gTUqQNBQRUtTeVHgyCVIqhwnQKVQ6+oTqncqA47d1auhEsvxQb5vPEGfPwx/PnPgNvjUxY4aviIyElgfL6iL40xO4EYYJeTfRWGr68vaWlpFZ4fIiXFuu9ycmzgVtu2qqjORlpammaBVQpQ0ToFKodeUZ1S+VEddu6sXGmnzpfu+ZE2l3Wg2dVX570XHg5paXDkiPUKOUmZruoyxjQC2gKxRVS5yBhz1BjzhzHmSWNMqQyxhg0bsn//flJTUyvU+j5xwioosI8nTlSYKJUeESE1NZX9+/fT0Om7W6l2lLdOgcqhV1SnVF5Uh5WcFSugy8XZ9P+oP81fbs7hlMN57xlTdl6fMgtuNsb4ArOAmSKyuZAqPwLtgd1ANDAHyAaeK6StwcBggPDw8CL7zM0MfODAAbKyskr3AUpBRgYkJNg9CI2xeQiOHaswcSo9vr6+NGrUSDM7K2ekInQKVA69ojqlcqM67Nw5dgx274bw//yNp39P4ZN+4TQKauRRJ9fwOW1v3VJTJoaPMcYLeB/IBP5RWB0R2ZHv5QZjzNPAoxSipERkOjAdoEuXLmcccgUHB1eKmy9/av8i9gBUFKWYVKROgcqhV1SnKNWJ1auh+4UnaDBzNsMz4MDtFxaoEx4O+/Y537fjho+xEYDvAI2Aa0SkuEMkASo+KtkhdNmvojiD6hSL6hSlOrFiBVzYvQ5jb7wK1zdf0+rSawrUCQ0tm6musojxeQNoB/QXkbSiKhlj+p2ar8cYEwk8CcwvA3kURanaqE5RlGpGbmDzh76beKE7XH7e5QXqNGhgd253Gqfz+LQAhgCdgEP5cmncbowJP/U8d0K9F/C7MeYksACYBzzrpDyKolRtVKcoSvVDBH5bmU54+33sSd5DcO1gosKiCtRr0MDGtjmN08vZd3Nm13JQvrqPAI842b+iKNUL1SmKUv3YvimTX463w2tEBCHtvenWpjveXt4F6oWGVgHDR1EURVEU5Uzs+XglV+bsxXtbALtnJ5CQkVRovbKa6lLDR1EURVGUcuPrtB7EPrydh24+RB3/utTxr1tovXr1bPLO7GybwsEpyjSBoaIoiqIoSn7WrYPzejYi5+KuZ6zn5QUhIZCY6Gz/avgoiqIoilL2ZGQgK39h3TpY5zONhi805M01b57xlLKY7lLDR1EURVGUsufttzHdLuX5jOGsjP+WhLQE6tYufJorl7IIcFbDR1EURVGUsicjg2y/QI5EXsyPu38EoHfL3mc8pSyWtBfL8DHGvGmMEWNM00Leu8AYk2mMmeqsaIqiKIqiVBsefpjJD+xi8zX1yXBlcFHjiwgLDDvjKRU51bXi1OPFhbz3MnAcGOeIRIqiKIqiVEt+2hTK8cbfANCn5dl3H63Iqa6Vpx49DB9jzLVAP2CsiBS+EL+as2IFPPecfayp6DVQFOfQ35Neg2rHhAmwYAGSI6xZK/yW/hkA17W97qynlsVUV3FXxv8BJJLP8DHG+AJTgI3AW86KVTVYsQJ69YLMTKhVC5YsqXmbCOo1UBTn0N+TXoNqx4YNMHYseHtzePkOXA2S2HNiJ40CG3HZeZed9fTQUNiyxVmRiuXxERHBen26nNopGWAY0Bb4l4i4nBWrarB0qf1xulz2cenSipao/NFroCjOob8nvQbVjshImDwZRo1i1cHz6NqiA78O+ZXp/acXuk3F6VSkxwes4XMNcIExJhG78/H/RGSJsyJVHXr2tCOS3JFJz54VLVH5o9dAUZxDf096Daodvr7wiN1Cb914iOls6NS4E50adyrW6RVt+OQPcO4B1AZGOCtO1aJbN+uGXbrU/jhrojtWr4FlxQq9Bkrp0d+TXoP8VGm9kpxsjZ6AgLyiVauFQfefac/hgoSGOr+q61wMn1VADnA/cDnwgojscFacqke3blXwhnSYmn4NNCahIIcPw+LFsGxZRUtS9ajpvyfQawDVQK/861/Waps1Cy67DBH4Med5jhz6Av9tY7m69dXFaqbC8vgAiMhxIA64AjgCTHRWFEWpmmhMApw8CQsXwogR0LGjndafOxc6dKhoyRSlalKl9UpqKvz+Oxw8aC0XYN8+yGj1CWuPrCDLlVXspurXh6QkyMlxTrxz3e90FdAeGC0iJ5wTQ1GqLjUxJsHlgjVr4NtvrWdnzRqIiYE+fWD6dOjSxb2b8oMPVqysilIVqdJ6JSAAVq6E1avhggsA+PSnjWSH/Upw7WD6tDp7/p5cfHygTh04dswaQU5QbMPn1PL1nsAaYKYz3StK1acmxCSIwPbt1tD59lv4/nto1swaOiNHQo8eEBRU0VIqSvWhyusVX1+4zL1c/cNN74APDGw/ED8fv3NqKne6q9wNH+AR4Hzg9lPL2xVFOUV1jEk4ehS++87t1cnMhN694S9/gddegyZNKlpCRaneVDm9Mm+etdQmTwY/t3GTkZ3Bb/I+APd1vu+cm80NcG7TxhkxzxjjY4ypb4y5zRjzHPAMMEVEVp6hfm1jzDvGmN3GmBPGmN+MMf3OUH+4MeaQMea4MeZdY0ztkn8URVFKQ1qaNXJGjYLOnaFVK3j/fRun89VXdo5+5ky4447yM3pUpyhKFSEtDR54AKZNg48/9njrf5vnk+WbQHSDC4lpEnPOTTsd4Hw2j09f4ENsMPPLwGPFaG8vcCWwB5v352NjTAcR2ZUvE40iAAAgAElEQVS/ojGm76n2rgIOAJ8BTxWjD0VRHCAnB3791Xpzvv0WfvnFBib37g1Tp8Ill1hvdQWjOkVRqgL+/naENHMm3Hmnx1v/+WUWAEO63oc7B3LxKVfDR0Q+Aj4qbmMichIYn6/oS2PMTiAG2HVa9buBd0QkFsAY8wwwC1VSilJm7NxpDZ3Fi238QMOG1tAZNgyuvBKCgytaQk9UpyjK2fnjD3jzTfjiC7vwwMvLLoV/6CFo374cBenSxR6ncWfALJL2fMLtHW8oUbNO5/I511Vd54QxphF2W4vYQt6OBubne70eaGSMaSAiHradMWYwMBggPDy8jKRVlOpHUpJnnE5KijV0+vWDl16C5s0rWsJzQ3WKorhJTYW//92mkrj3Xvj0U7vIID0dPvnELj64/HL473/tyqgy4bPP7Ajq8suLrLJxXRA3tbqX+v4l68Jpj0+x8/icK6dWgc0CZorI5kKqBAHJ+V7nPi/w9YjIdBHpIiJdwsLCnBdWUaoJGRl2xdWYMXDxxdCiBbz9NrRta+MODx6EDz6Ae+6pkkaP6hRFOcWuXdbWyM62ntznn7dT1S1bQlQUjBtn69Svb+vt3l0GQmzeDLffDn/6E2zcWODt4xnHSU5PZvXqQh1Bxaa8Y3xKhDHGC3gfyAT+UUS1FCC/Yz33ueYHUpRikpNj9U2uR+fnn6FdOzvSmzzZrgipXQ3Ce1WnKIqbbdtsComRI+00dVFhM7Vrw1tvwb//bXXBTz/ZRQuO0bo1DBlik+xERxd4e8qKKby88mUy0qbRtetdJe6m0k91ndq9/R2gEXCNiBSVojEWuBDIDf++EDh8uktaURRP9u1zGzqLF9u4nN69YdAg+PBDCAmpaAmdRXWKoriJj7dT1ePGWZvjbBgDw4fb1eX9+9u8go7F8vn4wMsv2xHYadZXSmYKU3+ZyvGM45wf2KJUeqkqTHW9AbQD+otI2hnqvQfcZ4yJMsbUA54AZpSBPIpSpUlOhvnz4R//sFtBdOoEixZZ7/Ivv8DWrfDGGza/TnUzek6hOkVRsCvGr78ebrmleEZPfh54wCZCHDjQBkCXmKwsmDTJCpOLV0FTYvra6SSlJxHhdRl9I3uUokPr8am0U13GmBbAECADOJRv2doQ4CfsXl9RIrJHRBYZYyYD3wP+wKfAOCflUZSqSGamNWhyvTobNsCll1qvzocfWsOnED1ToWS6MtmasJW4+Dji4uOIjY8lLj6OB7uWbr8K1SmK4mb4cBu3N2FCyc5/5RXo2xeeeQbGjy+FEK+9ZndR/d//Cq2SmJbIsz89C0DjbaPpcfW5L2HPT/36ldjwEZHdwJk+oUdSexGZAkxxUgZFqWqIQFyc29DJnYfv0weeftoGJvoXsRpixYryTWmfkZ3B1sSt+Hr5ckGo3YNnyY4lXD3rarJzsgvUX394fan6U52iKJYvvoCvv4b164uO6Tkbvr42KelFF8GNN9pB1OmcVaf8/e9WUT3+eJH9jPt+HAlpCfRs0ZMNr15L9xIaarkEBtoVbE5RpsvZFUUpnIMH3YkDFy+2QYh9+sBdd8GMGda1ezZWrLC5OnI3MVyyxFnjZ1P8Jn479JuHB2db4jZc4uLeTvfy7g3vAtCiXgtcOS5ahrQkOiyaqLAoosKiiA6LJjI0krd4yzmhFKUGcvgwDB5sl6iXNj6nWTM7U3XvvbBqlWeS0mLplKgou6LCp3DzYcPhDbyx5g28jBf/inyFYYGG884rncyBgXDyZOnayI8aPopSDqSkwA8/uI2dAwdsjE6fPjZIsSQrLZYutQrK5bKPS5eeu+GTlpXGloQtxB6xhs3oK0YTVMs6UYZ/PZyvt3/tUd/LeNG6fmtCA9yWWcuQlqQ8nkKAb8C5fwhFUc7KkCHwt79B9+7OtHfPPTBnjjWAnnjCXV6oTumSBfffb4MIbziVgLAIowesjri42cV0btKZ+I0dHZE51zjLynImm7waPopSBmRnw+rVbkPn11+ha1cbp/Pf/9q9sLy9S9dHz552VJY7OuvZ8+zn7D++n1dXvUrcURuLsyNpBzmSk/f+jZE30rVZVwCuOv8q/H3987w40WHRtG3QFn9fz3k3L+OlRs85sHUrrF0LO3bY1Sp33GFHtIpSGJ9/btPlzJnjXJvGwH/+Y6e6Bg60uX+gCJ0yZw689x4sWGDdQUFBZ2gZohtG8/PffibDlcGQ++CKK5yROdfrU69e6dtSw0dRHEDE/qF9+609li61QYi9e9up8CuucP7PrVs364rOPx9/MvMkm45u8ggyjg6L5vnezwOQ4crg+Z+fz2vD23gTGRppp6dCozw8OSMvH+mswDUcEbsH2sSJ9vtq2RLWrLEj7r//3T5Wgr3RlErEyZPwz3/CO+84n4/rvPPg4YdhxAibfBkK1ylcejts2mSDgs5g9BxOOUzDwIYYYzDG4Ofjx08/2VxDThAQYON81PBRlArkyBF3Lp3Fi+0fW58+dqnpW29Bo0Zl13dKZgq1vWvTrZsv3brB+KXjGfjKTHYd21Wg7qGUQ3nPI+pFMP7K8USGRhLdMJo29dtQ26caZDis5KSn25iKLVvsir3zz3e/t22bTVVwyy0we3b1SDipOMOECXDZZdbRUhaMGGFDdhYvtoM0sMZOt6ANp1K7h1j30MSJZ2wnJTOFHjN60KZ+G97/v/cJ8Q9h/36biqNdO2dkDQhwLs5HDR9FKSapqXbFVa5XZ/duu7Fnnz4wapTdFqKkqy2K4njGcTbFb8rz3uQGGe9J3sMv9//Cxc0uBqynZ9exXfh6+dK2QVuiG0YTFRpFdMNo2jd071LoZbwY11NXeJc3Y8bYOK+ffy64Qq91azudcdttNkfLZ59ZJa/UbP74w05HbdhQdn34+dk9+/71L/jtt1OhOwsXwk03WQto4UI753UGMl2Z/HXuX/kj4Q9qe9fGz8cPsMbUlVc6l3rDyZVdavgoShG4XLBunXvl1apVdhlonz42YeDFF58xxu+cSE5PJi4+jgxXBj0jegKwN3kv4f8ufAPNWt612Hd8X57h84+L/8F9ne+jVUgrfL11vqQy8eOP8NFH8PvvRaclqFXLhlLcfrsNZH3//fKVUal8jBxpjyZNyrafG2+EV1+F6dPtlCsdO9odTSMibEbmM5Cdk83t825nwdYFhAaE8snNn+TFAH7xhTXknUI9PopSRmzf7g5I/v57q3R697Yu4R49nNnhOC4+jmV7luXF4cTFx7H/xH4AOjfpzNrBawFoFtyMBv4NaBbczCPAOCosilb1W+Hj5f75tqjXovSCKY6TkmJX0Lz11tlTFPj4wLvv2s0c338f7ryzXERUKiHff28N5dmzy74vY2Dawzu56m8R3HGHIbhZM+v+OYvFlZ6dzn2f38fcuLkE1w7m6zu+zsvtlZ5udegbbzgnp3p8FMUhEhLgu+/cXp20NOvRueEGG4jatGnJ2k1MS8xbIh4XH8fgmMFEN7Sb+M38bSaTl0/2qO/n40e70HZ0btw5r8zLeHHk0SN4mUqWplkpNmPHWnd///7Fqx8YaP/seve22brbtClb+ZTKh8tlg44nTbJTUWXOlClEPfYYT1/yDpMm3WnDec5i9CSlJdH3g76sPrCaAN8AFgxcQOcmbt21dCl06ABhYc6JqR4fRSkh6ek2ziLXq7N1q11x1bu33eU4KqpkcTppWWmM/HZkXgzO4ZOHPd7v2KhjnuHTo0UPDqYcpF1oO6IbRhMdFk1EvQi8vQqub1ejp+qSkGBTF8TGntt5F15oDaY774Tlyyvf9iRK2fL++/ZPfsCAcuqwfn3IyuK2DhuJeBOGDuWsCQfr+tWlcVBjIupF8NlfP6NTY88U0J9/Xnxjv7iox0dRiklOjk3xnmvorFgB7dtbr87LL8Mll5w1dg8RIT413gYYH3EHGPt6+/Ltnd8C1mMzY/0MUjJTAAj0DSQqLIp2Ye2IDovm0uaX5rV3bdtrubbttWX2mZXKweuv25xvJfEaPvig3ZdtxgybuK4mc/SonXlJS7P5saKiymYhQWUgLQ2efBI+muNi/4mD7Du+j6OpR0lMS+Rk5kkyXZlcf8H1nB9ilwXGHolle9J26vvXp2FgQxoFNiK4djDmTBfnwAG7vPBPf7Kv774bOnakTufODA2xgfjvved5iivHxTfbv6FJnSZ0atwJL+PF+//3Ptk52TQIaOBRV8TG93zzjZNXxr2c3QnU8FGqHbt3u6euliyxA5o+fWzg3iefQN26hZ8nIhw+eRh/H3/q+tlKb615izHfjSEhreAOeX4+frhyXHh7eWOM4fVrXic0IJR2Ye0Irxuu3poaTFqaDRhdurRk53t5wbRpcN111nhyIndJVSIz065o+vBDu6qpc2ebQsbb28a+nDhhr82jj0J0dEVLWzqS05NJTEvk/JDzmTYNLujxO1ct6ULWt1mF1o8Ki8ozfD74/QOPvFwAQbWCOC/4PDo06sCcAe6sh78f/p0mB1MIvbwPJiDALhsLObVcvbOdpnrsMbjgAruQI6pTCiv2ruC7nd8xa8Ms9h7fyyXNLmH5fcvxMl55OvJ0fvvNTtFFRjpxddw4uW2FGj5KlefYMRunk+vVSU62eS/+/GeYPBnCT1sYJSIcTDmY58GJi4/Ly2ScmJbI9OumMyhmEAABvgEkpCUQXDs4L8lfdMPovGmq/MbNnRdqNKpimTnTehNLk8OkSxc7XTB+PPz7346JVun57DO7mql1a+v96NmzYKzLgQPWG9arl111PW3aqbQzVQBXjosV+1awcOtCvt7+NesOrqNfm368f/VXvPACfLO0FTFzs2kU2Ijz6p5HWEAYDQIaEOgbSG3v2kTUi8hr64LQC7i2zbUkpCVw5OQRDp44SEpmCpuObqKW9ylXdlYW4uPDJW9fQnpWOj+FGVKChX+/3ROaNCGwViAPdHmA3i17U6cO9Bk9nSvmTSB70X6PrO4tQ1pyY+SNZOdku9suhM8/t6u5nPbIqcdHqdFkZMDKle58OnFxNslXnz7Wo9Oxox0xiwj7T+znm+1xHEo5xF0X3pXXRrvX2nE843iBtuvWrsvJLPew4obIG9g3fB9N6zQ9s/tYUU6Rk2Nzo/z3v6Vv69ln7dTO0KHOj6ArGxkZ8NBDdvn/a6/ZgUtRNG1qM6IPHw4vvGAdFi+/bLdfqKw/03UH1/Gftf/hs82fecQA+nr5IiI8+6xNn3NRdCCpF6Tm5cM5E/d0uod7Ot2T91pESEpPYm/yXjKy0+281bvvkrJqGZGhkexN3kufOxJI902D1N9h++8AXN/Wve78sm6G977ai5d407VpV3q06ME1ba6hZ0TPs3qxs7Ptff/JJ+d4cYqBenyUGoWI3Qw4d/pq2TL7J9C7Nzz/vB3x+fnBHwl/8OUfX/Lql+7dxHONm9retRnYYSA+Xj4YY+ge3p3jGcet5yZ3qXjDaJoENfEwcIJrBxNcu5TbIVcHcnJsZLifnzvadu9ee4SHu4fbBw7A/Pl2OUe5RWdWLpYvt9mXL7+89G2FhcEjj9hg548/Ln17lZVDh+yUXqNGdo+74qaN8Pe31+a662wweK7R5FR+LSf5fuf3vLn2TQDOr3c+N1xwA31b96VHix7EHwig8z+tngOKZfQUhgHq+9envn99WxD7HBw6RJ0Fi/l1yK8ApGalcjjlMEdOHiEhLYG0rDRimsbktXFz9E2EJPXi4fubs3hDrXPaDf6zz6wq6Nq1ROKfkYAA6913BBGpUkdMTIwo1Z99+0RmzBC5/XaRRo1EWrYUGTzEJW98uEvmrF0gL/z8gtz7v3vls02f5Z3zwfoPhPF4HA0mNZAr3r1Chn4xVJLTkyvwE5UBOTkiqakiKSnusuxskRUrRH74wbPu/PkiU6aI7NrlLvvmG5G77hKZOdNdtmePSMeOIn36eJ4fGSkCIps2ucsefdSWTZrkLvvxR1t2+eV5RcAaqQS6o6jDaZ3y4IMiEyY4115KikiTJiLr1jnXZmXi0CGRCy4QefJJEZer5O0cPy5y9dX2OH7cOflKwqp9q+TWubfKsz8+m1d28MRBGfnNSFl3YJ3k5OR41L/zTvv5S8W0aSJt2ohs2OAuW79eZOXKEjV3330iQ4ac2znduol8+mmJujsrb7zhlqe0OqUS2sVKTeTECRsI+u238O1iIf6I4aqrrFfHt/8wYo+vYFZ8HNP/OAl/uM+rU6sON0beCEDXZl35e5e/e8TghAWEsXKlYelSiG1watO9siYz005GBwW5h5579tjtuMPD3VshHzpkk7Y0aOCZre6hh+xGYG+/7R765g75J0xwe1I+/RRuvtkOlT/91Ja5XPZD+vhAVr7gyNdfh6+/tq6yFqeSHW7dapdvBATAXe5pQH7/HZo18/xM/v7W25OR4S47/3ybbCb/pmTNm9vUw23bluzaVXGys62b/+efnWszMBBGj7a3wBdfONduZSA+3sbp3HYbjCvlTip16tj4kgcfhKuusrqkrILCV6w4bSNPrBNh0bZFPP/z8/y4+0cAfg7+mVHdR+FlvGgc1JhJfSYVaGv9ersCauvWcxRi715o3Ni9s+2mTbaRDz+0c6Rg5/1LyEsv2Vw8+ffxOhMrV1qVdsMNJe7yjDgZ4+PoyAn4B7AGyABmnKHePYALSMl39CxOH+rxqR5kZor88FO2/HP8Nml3w+dS66rnpPEDd0qzp2IkeGKIZGRl5dW9/J3L8zw4jV5oJH+a8Sf5x1f/kNdWvSa/HfztjP0sXy7i7y/i7Z0j/v45svzrfEPBnBzrGfn6a8+T5s8Xef55kT/+cJd9953IbbfZYUcuhw5ZT8gll3ie36mT9XqsXesuGzvWlo0b5y5bs8aWde7seX7TprZ83z532dChtuz1191lX30lUru2yE03eX6mSy8VufJK6/3J5fXXRYYNE9m40V22aZPIf/8r8ssv7rLMTJFffxXZutVTptNGqOcCpRidVTWd8vXXIl27lr6dLFeW7Dm2RzbHb5b1h9bLH4d3y3kRGbJiRenbriykpNhbf/ToUt1eBcjJEfnnP+3PMrkMnLxunWIff/45R+Zvni9dpnfJ01PBzwXLyG9Gyu5ju8/aXt++1llzTtxxh9UHixa5y+LirE7IpztLy6JFIi1aFM+DdsstIv/+t2NdF2DuXJG//MU+L41OkTLw+BwAJgB9gSJ2pcljhYh0d7h/pRLiynGxPXEHe3b5Erc8wi4z37OQtP434ZeTRlAbED845AMIhMfDkf+9R/P2l0FkJBOvmkjtxON0WLiWwOCmcPdgd+P/+Afs3283mslNE/r003bJx7hxLD1wN5mZ4HIZMtOyWPrQp3Tbco+tZ4wdGrpc1kuTO3KaMcNOVrdp406du2uX3XCpVi0baQrWq7J5s10Smp+6dSE42NPj0rKl3fMif2awJk2sd6fFadtN/Pvf1nWQf7g6Zgz885+eSWGuucbG3eTHGDscPZ0HHihYFhlZMGLW1xc6dSpYt+IiRquUTvnoI+u9OFdcOS4S0hJoGNgQsEuPY6bHeFa6B3p+3pxrdnfl8Ssep0vTLqUXuIIQsbvVt29vN/528vYyxv6EHnwQ+vWz3pTAQOfaX7qUUzrFPr49bxv/rWPdHA0DG/JIt0cY0mVIsWIDFy+Gbdtg8OAzVHrrLVi0yK7vz9335PzzrQtk5053vXbtnNsK/RR9+9rjzjth7tyiY6d++MFel7ffdrR7Dyqtxyf3wCqqs43OlpWkbfX4lANZWSLx8SJHjniWL1ki8vnnnp6E+fNFnn46b155a8JW+eG9CbKpR5S8O/AiCX/2QvEaW1uCH0O2BQXLvnpR8tFHIt/HrRfGI6siaomA/PuFAfLWmrdk2e5lcvLpU96RkSPd/cTG2rLISE+ZWrWy5fm9M8OH27IXX3SPzrxc4s9JWX7FSM/z//xne6SmustmzLDxK7/l8yZt3y4ya5andyQ723pQdu4s8lIuXy7y7LP2saaCAzE+VUGnpKeLhISI7N9f/HNSM1Nl8rLJ0vjFxnL1B1fnladlpUnzKc2lzdQ2EvValDR5sYl4P+Wd51FYvsd9Q63ev1o2Ht5YWPOVlmeesR6ZtLSy68PlErn7bpFrr3XUCSLLl4v4+bs8PD7XzLpGXl7xspzMPFnsdrKzbTjd3Ln5Cv73P5GJEz1dYL16WX02e3Ze/88+mSrLv0937kOdgYwM65W6557CY7B27RJp3NiGDJYlS5eKXHGFfV5anVKRhs9J4Cg2YuNJwKc4bddow+fYMZG9ez3/pHftEvnySxvElktCgo2ufPllz/P/+U+rBfbudZdNnCjSrJnIa6+5y777zt4aPXp4nh8UJAKSmRAvm+I3ydzYufJ774627vvvS0qKSPSL3eWWAYiAzIlyBxlHTGxm6/n5iYh15SelJYn07y8SGuoZjPvxxyK9e4u8+aa7LD5eZMQIkZde8pTpiy+s5sjv0z50SGTbtjz/bEUZH6e7xGuq8VOOhk+F6pT58+0MY3HIycmR9357T5q+1DTvN3LBtAskIzujyHOyXdny5CubpNNd70lqplsH9JzRUxiPXPKfS2T2htmS5XLwX74MWLjQqpxzMRBLSmam/dMeNMiZ6bQ9x/bIHfPuEN9BPeSRJxNK/ptOTJSl97wrL7Z+wy1XTo61nEFkd74psvnzRd55R+TAgQrTKSkpdgZ98GCRxETP8k6dCqrlsmD1apHcn2pVNXxaAucDXkAHIA4YfYb6g7Hz/GvCw8OdvZqlJTPT/oJP/xV/8439Q07PZ5XPny/yxBM2tiOXn38Wue466zXJJT1dpHlzG+uRn9697VeWPybllVds2T/+4f6D//SALTv9WnXoYMvzG0mPP27LnnnGXbZqlf0BXnutiNgf+/jvx8vKi5vJ9+2DJHS0T56yvnkAsvDKIXJf53USFCQSfs+T0n34lfLyg/1l3ownZOXelXY1VU6OjRvJH7dSzXn2WaugwD4+++zZz6mOlJPhU+E6ZfDggmONwkhOT5aBnw7M+w1d9OZFsnDrwgIrfQojLc2qhdwVXtmubBn6xVAJfi44r70WL7eQV395VdKzSu8RcHrQcPCgXaG2dKkz7RWHEyfsH2Z+FXeupGSkyJPfPSl+E/yE8UitZ2rJrN9nFX1C/u/yl1/scqR8A7kTG3baQWSDxp7njRol8thjnoPTfFSkTklIsF6f+vVtuOAtt4jUq2c/mpMxWkURG+t2+FdJw6eQ+rcCa4tTt9ijs4QEOz1x4oS7bNcukXnz7B97LseO2XWEp68/HTbMLunNP4UyebL1TuRfvvvLL/Yynh7R2KiRLT940F1233227K233GXz59uyU0aGiNi7yE6De/oWBw60WiO/T/HLL0X69ZPlI+bmGwnkyPK73rDLl/Pz7bd2qurYMY/rlL5jq2zc8YvM3jBbxn43VgZ8PEAm/OC+HhsObyiwTDzg8Rbic/c1EnrbI/K3h3fKggWeq6oV9fjkUh6GTyH1ndcpZyAnx44z8q/2L4xjacek9dTWwngkcGKgvLPuHXHlnNsa7ilT3EGeuZzMPClvrH5D2kxtk/cbbT6lufy85+dz/CRunL5/XS47q/zEE6VrpyQcPGi/nzlzzu28nJwc+WD9B9LspWZ51/Wvn/xVdibttBdk9mw7F5TLyJEiDRqIfPihu+yTT6wu798/r+jxx1yyrOWd9n8nf+jAWagMOmX3bpExY0Teftvz762s2bXLPZavLobPX4F1xakbExxsreJccnLsBGNwsKeR0L+//Xj/+5+77D//sWV/+5u77PBhWxYa6nmVL77Ylue/syZMsGWjR7vLYmNt/1df7Xn+3XeL/N//ecbJfP65yFNPeXp8Dh60xk/+MhF7dx05UmxTujgjgfSsdMl2uX9kY78bK5GvRnrEDuQePf5rp7mOHBH54KMM6fDwSGnQa4aEdlwtA+9JkQ8+KN+bvqqiMT4VZvgUX6c4YPjExVmlXJyf68QfJ0rHNzrK5vjNJerr5EmRhg09F+jl4spxydzYudLh9Q5S97m6cvTk0RL1IeK8d+Gll2yeFyfjbc6F334TCQs7S1qbQ4dEvv8+7+I++s2j0mIYsqgV8k2XEFm2e5m7bni4vTjbtrnLRoywZfkv1u7d1jP/008iYo3j0NCST/XVVJ1y5Ii1KUUqmeGDzQTtBzwHvH/qeYF5dqAf0OjU80hgIzCuOH3EgMhVV3leEX9/+1HyuxwGD7br8L780l22ZInIDTd4rh1MS7NLjE/3Uf/0k51SSkpylyUnW0Mpf4xNJcFzJJAjM77YIrN+nyVjloyRG2ffKG2ntRWvp7xkw2F3cqsHvnxAGI+Y8UZaT20t1390vTyyaLSMnPW+3D1yvVx0kbUnr7vO/m7j4srHpalUL0qjpMpFpzhg+EyZYlVOcTlTLE9xmDjRrmguCleOy8OwSs9Kl1vn3ior9xY/mZ2T3oW4OPuntX17ydsoMS6XyIIFIu+/L198YZ3mu3aJHUB37pxnkIiIyNSp9r/k738XEZHN8Zuly9gmIiA5DRt6tjtokHW95Td8Dh+2I8IiMjHm5Ni/r7Jc9l1dOXnS3ocilc/wGQ/Iacd4IBybVyP8VL0XgcOnghF3AE8DvsXpI6ZNm4IpTA8dstM3Nexf+WTmSVl3YF2eMlu+XOThJ+LF3H9ZAQ8O4xGvp7zkiy1f5J2/5egWWbPvV1n2S6o895xdPBAUZJPujhsnsmyZDWFSlNJQSsOn7HWKA4bPn/9sZ9ELY1/yPuk1s5dsS9hWeIUScOyYjbUoriHxyspX8vTAHfPukH3JxYu1c8K7kJVlHej510+UCJfL06BYudKOyFavdpctWybSurXIzTe7y3JyRHx97d9dWppMmWLDHTP/8ldbNsvG6mS7suWLVx6U2MgGkjN5ct7pmempdgDtQOrsWbNsMHBFeb2qMi6XiDH2sbSGjxGrNOJmzMkAACAASURBVKoMXbp0kTVr1lS0GOXO5qObWbV/ld1JPN7uRbUzaSeCcEX4Ffx4r80UmunKpO7zdWlRtwXRDaM9dhO/IPQC/Hz82LnTvcHnd99Bw4Z2g88+feDKKzmnvVkU5WwYY9aKSKVNOlNanZKaapNX79tnUzh5vJeVypUzrmTNgTXcGHkjn/31s1JK62bMGEhIgDffPHvd4xnHee6n53h55ctkuDII9A1kzBVjGN5teIn3hSoukybZpOGLF7u3ecsjJ8dmA/c/laIpOdnmqxGBRx9117v8cvjlF7uZVW7uqcces41PnGh3LAVYtQouuQRiYiD/d3rbbeDtDa++itStx9Ch4L05lmmTUvGObMNPyRt4aOFDrD+8HoBv7/yW3i2Lka74HEhMtHmL5s2zCc+Vcycw0Ca1DwoqnU5Rw6cSkZKZwqb4TXmGzZCYIbSq3wqAhxY8xKurX/Wo7+PlQ5v6bbj8vMv5z/X/ySvPcmXh6+2b9zox0Ro4ixdbY+fkSZuCPPfI3V9SqX4Ullq/vKnuhs/ChXaz3B9+8CwXEW6fdzsfbfyIiHoRrB60mtCA0FJK6yY+Hi64ADZsKLjDSFHsSNrBI988wmebrQHWKqQVr1/7On9udYat0EtCdjb4+LB5M3TvDhuf/5LGe1bBLbfYf3+AmTPh/vttJsPp023ZkSPWiqxf31p1uVxxhd2d+KefbIMAX35pE/tddx1cfbUtS0uz28M0anTG/Sqysmxyw+bRe8nsMYqPNn4EQHjdcKb8eQp/afcXj82KneDWW61Yr7ziaLPlTkXqlLAwiI2FRo1Kp1N0r64K5ETGCZ764ak8L87u5N0e71/U+KI8w6dHix4cST2S58GJCouidf3W1PKuVaDdnGxfvvvBbehs2WIHTH362Gym7dtXZCJepbxYscLug5SZaRNOL1lSccZPdWbRIvf/bn7eW/8eH238iKBaQXxx2xeOGj1g/wTuvhtefBFefrl457QMacm8v85jyY4lDFs0jNj4WI6cPFIyAeLj7eZhfn4wcGC+TlrCrl3kJCUzaFAdxo6Fxktnw6xZ0KqV2/CpW9caSMePu88NDYV//cvuQSXiVlSff26H+7Xy6bvrrrNHfvz9rTV4Fnx9oefjLzH2+7HIxlT8fPwYdfkoRl4+kgDfgJJdjzPw0Ud2T6516xxvulypaJ0SGOhM9mY1fMqQ5PRkj6mpuPg46tSuwyc3fwKAn48fU3+ZSlaO3dqglnctLmhwAe3C2hEdFk2HRh3y2ro5+mZujr650H5ycuyo79tvrbGzfDlERVlD58UX7Y1Zq6B9pFRzTk+tv3SpGj5lweLF1nmRn33H9zFs0TAAXu33Ku0bti+Tvh991NoRjz3muVfs2ejVshe/DvmVT+I+4bb27j02vtjyBVekN6Te/gQ7H1O/vn3jnXfghRfgvvvcU1D79tnXHTp4Gj6njJXZrxwmO7sODz4INL3RGkQd3Dotb8uV2rXdZV5ehVtxp28L4wQ+aYhPKv47bmZS78k81DPC+T6wO+oMGwYLFrhn9KoqFa1TAgLsjEVpUcPHAZLSkqjlXYvAWnZDmNdWvcZzy55j/4n9BerW86tng6uMwdfbl1eufoVGQY3yPDg+XsX7SvbudXt0liyxg6feve3G2LNnl92uxErVoWdPa/Dmjs569qxoiaofR4/a///825uJCPd9fh/JGcn0b9ufuy68q8z6b9oUbr/d7qQ9efJZKmdlQUpKnhHhm+Vi4Ks/QMI8mDuXHUk7GPDJABb/N4crdmSTtfArfK++xp6bkWFdx9u2udtr0QLuuqugh2XlSvafrMewrr4sXWpDaxgwwB75KefR2Hc7vyMxLZEBUVaOEd1G0KNFD+ol96BPH2hZH6691tk+09Ptxx42DLpU2sne4lPROkU9PhVAYlqi9d4cic3z4MTFx3Ew5SAf/N8H3N7xdsDG3uw/sR8/Hz8iQyOJCosiOiw67zE/D3QtZPPIQkhOttZ1blByYqJ1OfbpA889V3CfS0Xp1s0axRUd41OdWbbMXtfTN2+8vu31bIrfxPT+0x2PFTmdUaOgY0friAkLA37/3QYCx8RA58620tdfWw/L1VfDV1/Zstq14b337L/ziRNk52Rz+XmX81PT70kD3lk4iJvOe5mbo27GDBhgN9kND3d3XL9+QVcXIKFhPDjI7osbHV3g7XJn7YG1PPH9EyzatojQgFD+3OrPBNcOxt/Xnx4tegB2xu666+DDD+0A0glE7EC0eXMYPdqZNiuaitYpTm1UqoZPIRxNPUpcfBzxJ+O5KeomwO6e3PSlpmS4MgrU9/fxJzEtMe/1gKgB9GrZi/PrnY+3l3eJZMjMtLor16uzYYO9yXr3th6dCy8sZIWEopxGt25q8JQlP/5o7YH8GGN48OIHub/z/dT2qV34iSUhK8sG/+aPZB4xguYrV/Lg1e8xZUornnsOG1Dy/PPw1FNuw6dRI/tPnJ6eX1AbVFyvHvj60rZOW5bctYTPL/mcfy4exZaELXw8969MbjKZZ/70DP3a9yuWmPPmWefQnDnOffSS8Nuh33j6h6fzArnr1KrD8EuH4+vlW6DuxRfDp5/CTTdZW65f8T7qGXnxRWuDLltWvXR1ReqUwECd6nKErQlb+Wb7N9Z7c9R6c+JT4wEIrh2cF93v7eVNTNMYMl2ZeZ6bdqHtiG4YTUS9CLyM+85uENCABgENzkkOERutvnixPX76CVq3th6dZ56xwcl+ZbvqVFGUc+Snn2DKFPfrTFdm3oKDEhs9Bw/aJWL16rmjphMSrPHy/+3deXxU9b3/8deHJLIEkB1RQUTAYApBNouUi/wAwd4KKK2iomJrqfaBXi2X61KsC16trddqq7XlulCl4lXq1vbeVqukbkEWARGsqagssu+LSCT5/v74TkiIk5BMzsw5k3k/H488yExO5nxykvnwOd+1RQvYubPi2KVL4e23ueaqj+h13Slcfz10GDIEJk8+sv+td29f9FTtXrr00iMemhnj8sbxrz3/lceWPsathbeyZOMSZr07i3N6HL0a2LULrr3W35w1DrDmq4udB3Zy2QuX8afiPwH+xvSaQdcwfcj0GgeYDx0KL74I553n68bJkxOP4b774KGHfGGcm5v468iR1OJTS845Nu/fXDHIeMtKzut13uHpm4WfFjL1/6Ye8T3Nj2l+uKg5cOjA4VH+b333rUBj27ChotD52998ohg1ynebz57tJziISDTt3QsffAADB/rHa3atYfCjg5l+5nSu+/p18bu4Dh3yt//lTQBz58K8eX5Kd/kMpcWL/bozo0dXFD5t2visX37LW/6/6cyZcOgQHfr2ZdJiuOsuuP/+OLOdsrJig21qJ7tRNlP6T2FSn0k8vOhhRp0y6vDXFqxfQPH2Yi7Mv/Arxd0NN/hTDx1a61MForSs9HDreqsmrVi7ey1Ns5ty1YCrmH7mdDq16FSr1xk82HfjnHOO/93OnFm3oUjO+e+ZM8cXPZV7BqX+NLj5KK7/y/Us3riYVVtXHdENBf6NUV74DDphEFf0vaJiDE6HfDq37JyUfvm9e/2NXHn31caNMHy4L3Z+8hM/01PTzEXSQ1GR70kqb4m9+bWb2bhvI4vWLcBafwibN/sVQcuNHOkTwIoVFYvwrVzp+4by8yuKlV694Pzzj+xPMPOtPjlVummGDDn86c03+9mcP/pRcP/hNstpxrQzpx3x3IzXZvDqJ68y/ZXpTOk3hStOv4JurbtRWOiHD73/fjDnro1Pdn7C7GWzeXTpo8y/fD492vbAzHhi/BN0atGJDrkd6vyaeXl+mMGVV/pfwZw5/ldyNJs2+XFNn3zii57jjkvgB5IaZfTg5s/2fHbEFPGVW1eyfs96Pv23Tw8XLIVrClm2aRkAxzY+9ogBxsO6ViSjguMKeGzcY0mJ89AhWLSoYkDy0qW+L3nUKN+i069fnW7CRCRC3ngDxvdeDfc+z4YWMHfTXI7JOoZ7+t8I3Xv5bqnduyvuZho18klh7dqKwuc73/Hz0StP+ene3Q84qapq0VNFx45w1VVwxx3wyCMB/ZBVOOe4uPfFbP18K+9tfo8737iTO9+4k3/pPJwPnp3ILx48n1atkttUvWHvBl78x4s89f5TvLn2zcPPP7vqWW4e6ldwLjiuoF7n6NDBd3v993/79RLPPde3ZsUrgHbs8EsU3XmnL5bC7OZr6DK2xWfZpmWc+Iv4Sw2v27OOLsf6W527R9xNlmWR3yGfTs07JX1mBfhmzuLiivV0Cguha1d/ozdjhm/+bRb82lgikgwlJX66Vnm31OOP+//hrr4aJkzg9dfhvhH/gOnT2VnQCXeeY3LBZDp36+tnH3Ts6FcSLn/TP/GE3w+mchIoKPAfAZk+HXr0gOuvT86MKjPju6d/lyv6XsHra17nkaWPMG/VPF5fNx++Pp+dx5cAfujAzgM7yT0mN+4iq4ka//R4XvzwxcOPm2Y3ZXzeeKb0n8Kwk4bV8J11ZwZTpvja9KGHfONdu3b+5rVzZz/Uas0a37ozZoxfp6d//0BDkCoytsWntKyUNk3bkN8+3w8wji32d1r70ziueUXb4pjucZZSTYItW/z0vvJixznfonPBBfDb39ZtUTERCUFJie+3qty1NGoUzJ/vl9stryA+/dS/2QcN4uC3JrBkCZz6mz7s+Wwy9257gkbWiBu+cYP/H3PZsq+eJwV9H61awS23+HVjXnkleV3nZsawrsMY1nUYl7T+FRfe9jwDL3+WCb0mHD5mxmszeHTpo/Tr1I/eHXrTq30vTm51Mse3OJ4ux3ahY3OfHEvLStl+YDu7v9jNlv1b2LB3Ax/t+IjiHcUs3biUly99+XCXVe4xuTTJbsLZp5zN+Xnnc36v82nRuEVyfsiY1q39jeuNN/puvHfe8d1ap57qZ/Q9+aTWTUuVZs2OHNufqLQrfPoc14dl05fVugUn6H1FPv/cN3GXd1+tWeNfe+RI3xTas+fRk00U9k8SkZgVK3yhs3dvxZs3J8cvib52bUXhc9FFfgPMggJ+9zvfeLNiV2fmjG3G7MVlXPK1S+jWulsoP0LlnHL11X6W+gsv+BlKybRnD/zwu6148v4rGDv2iiO+tnn/Zg6WHqRofRFF64uO+Np5eefx3IXPAbB652pOfbD6bSYWb1jMN3v4hRTvGXkPs7416/BisamUne0nylWeLCeplZvrV8Kur7QrfHIa5dSp6KnvviKlpbBkScWA5EWL4PTTfZ58+GHf7Fl18bJkxyQiAWrSxI+x2bvXVzPgB+G1bHnkGhJ5eZCXR1ERTJ3qh+uMGOHodl0JNIabvhHOKnXxcsoDD/jxJmPGJHebhOuu8+ceO/arX5t3wTx2HtjJko1LWLV1FR9s/YC1e9ayce9GOrfsfPi4JtlNaNesHc2PaU7H3I50bN6R7q2707NtT/I75NO/U0X/0YkttaNyJsvYMT51kci+Is7B6tUVhc78+X5Z+JEj4d//3TdttqjUslrX1puw9zpJJ2oZk5TIz/d/aJV1qH42UGGhX0sQoKTEuLj5LM6e/APyOwQzqCaInHLTTX68yV13+enVyfCHP/jW76VLqz+mddPWjOw2kpHdql8OucuxXdg6fWsSIvwq5ZT0lrFjfOqitvuKbN9+5Didgwf9Xcy4cfCrX/nCJ55EWm/C3uskXahlTKLqrLN8j1ijRv5vc/hwY8DxwWzEFGROeeAB3zo9dmzFWkNBKS72XWp/+hM0bx7sayeLckr6U4tPLVS3r8gXX/hlxMtbdT76yLfkjBzpZ0P06lW7QYGJtN6EvddJulDLmERVjx6+++h7/7aJYcPKGDy4mjujBASZU044AX75S78487vvBjejdN8+v8zQzJm+qz9dKKekP7X41NLgwX484vLlfvfiV16BBQv8Cu6jRsH99/uvJ7JRcKKtN9o/6ejUMiZRtXChf/9+eNrlPLjgFZ7t/OzhPf3qK+icMnGiX4/mxht9EVRfZWV+7NCgQX6qdzpRTkl/kWzxMbOpwGSgNzDXOTe5hmOvB24AmgHzgKudc1/dATRBa9ZUdF29+iq0besLnalT/Qrxxx5b/3Oo9SZ5dG0FopVTyi1cCN3P+Ce/Xf0yTbKbMPzk4YG9djL+7h96yI/d7tevfvtPOQfTpvmJbq++mn6rzCunpL+otvhsAO4ERgPVziUws9HAjcD/i33P88DtsecSsmuXH4hcXuzs2uW7rkaPhp//3C84lQxqvUkeXVshxJxSnXfegSbnzoKtcNHXLqJN0zaBvn7Qf/dt2vjF9YYN83lwxIjEXmfmTHjtNV84JHOmWDIpp6S3SLb4OOeeAzCzAUBN8w4vBx51zq2MHT8T+D11SFIHD/rBauXjdFat8tvWjBoFP/iB78oqX3BVRNJTKnNK7eKBdxaVkjN8DgBT+qdHf09eHjzzjF+F+M9/rttg57IyuP12eOopPzaydevkxSlSk6i2+NRWPvBipcfLgY5m1tY5t73qwWY2BZgC0Lp1HuecA2+95d/MI0fCT38KZ56p/VHkqzR9NWMknFO61GFHz9WrIbv7a2w5sInubbpzxgln1DPs1Bk2zO/h9c1v+tmqEyce/Xv27YPLLvMrFb/xhlaiL6e8Eo5ItvjUQXNgd6XH5Z+3AL6SpJxzs4BZAO3bD3BXXum3zGkTbAuzNDCavppREs4pAwYMcLU9yTvvQNOv+9aeSb0npWQPwCCNHetbyceN8++Pm2+OX8yUlfl1en78Y79J59y5urEsp7wSnnQvfPYBLSs9Lv9879G+8aSTYEIwEyikgdP01YyScE6pi0WLoH27RmymMZf0uSTIl06ZggI/QPv22/3SHRMn+vdFt25+C4qFC/1MMDPfMnT22ek3kDmZlFfCk5MDWVm+MK+PsEbBrAQqb0lcAGyO1yQtkqjy6atZWZq+mgFSklOWLIF7Bj/Otv/YRvc23YN86ZTq0MHP9lq5Ejp18oOfp02De+/165z953/6Im/0aBU9VSmvhCuI9aiCns6eHXvNLCDLzJoAh5xzh6oc+gQw28x+j5+BMQOYHWQsUncNrd9a01fTX5RySlmZ33S9Xz9ofkyaLFd8FJ06+d3ck0l5RYKUmwu7dx/9uJoE3dU1A7i10uNJwO1m9hiwCjjNObfWOfcXM/sZMB8/RfUPVb4v7aXbm72h9ltr+mrai0xOWbJyF7kF75DbcjiQwIqn9ZRuOQWUVyR4kWvxcc7dBtxWzZePuEVyzt0H3Bfk+aMiHd/s6reWKIpSTnns7ZfYPOpyvv3Mubx00UvJOk1c6ZhTQHlFgpebW//X0Eo3SRDvzR516rcWqdnf1j0PwOhTRqf83OmYU0B5RYIXuRYf8dJxTxj1W4tU7/MvP+fjRn8FYFzeuJSfPx1zCiivSPCCaPFR4ZME6fpmV7+1SHx//ehlyrIO0LfDQE5sWdMC0smRrjkFlFckWNOm+bWo6kOFT5LozS7ScMxZ/AIAF3ztvNBiUE4RgTFj6v8aGuMjIlKDQ2WHeHnNHwE4r1d4hY+IBEMtPiIiNVi3ex05X7ahXaP25LXLCzscEakntfiIiNTg5NYn07+omAcK3go7FBEJgAofEZEaOAdL3zWGDWwbdigiEgB1dYmIVGPPwT0Uf7qPrKzjOf74sKMRkSCoxUdEpBrPrnyWgU+fQOPx12izTpEGQoWPiEg1/rraL1p4atteIUciIkFR4SMiEkdpWSl/+9ivlPbNnqnfpkJEkkOFT5orKoK77/b/ikhwFm1YxM4vdpKz9xRGDzol7HBSRjlFGjoNbk5j6bpjs0g6+MtHfwHA/XMMPXuGHEyKKKdIJlCLTxpL1x2bRdLBy6tfBqDrodFkZ8gtonKKZAIVPmmsfMfmrKz02rFZJOq+OPQF7258F6MRZ54wLOxwUkY5RTJBhtzHNEzpvGOzSJQ1yW7ClulbmDTtPQYVtAw7nJRRTpFMEHiLj5m1MbPnzWy/ma0xs4urOe42M/vSzPZV+ugWdDwN3eDBcNNNSlDScIWVU1o2bsmmhd+gb9/EY09HyinS0CWjxechoAToCPQF/mxmy51zK+Mc+z/OuUlJiEFEGo6U5xTnHKWlxsqV0KdPfV9NRKIk0BYfM8sFJgC3OOf2OefeBF4CLg3yPCKSGcLIKftL9tPl/i6MfWIix3Uqo0WLZJ1JRMIQdFdXT+CQc6640nPLgfxqjj/XzHaY2Uozu7q6FzWzKWa22MwWb926Nch4RSTaUp5TitYXsX7Pej7Y8k/6Fmj+h0hDE/S7ujmwp8pzu4F490zPAL2A9sD3gZ+Y2UXxXtQ5N8s5N8A5N6B9+/ZBxisi0ZbynPL3T/8OQPt9Z2Xc+B6RTBB04bMPqDoFoiWwt+qBzrlVzrkNzrlS59zbwAPAtwOOR0TSW8pzSuGaQgBKPx5GQUGd4xWRiAu68CkGss2sR6XnCoB4gxCrcoD2PxaRylKaUz7/8nMWfrYQw/js7aEqfEQaoEALH+fcfuA54A4zyzWzIcA44Mmqx5rZODNrbd4g4FrgxSDjEZH0luqcsvCzhZSUlpDfroCDu1vTpUsQP4WIREkyRu79EGgKbAHmAlc751aa2VAz21fpuInAR/gm6yeAe5xzv0tCPCKS3lKWU4rW+Z05u2UPoU8fMLVBizQ4ga/j45zbAYyP8/wb+IGK5Y/jDjoUEakslTll7KljyW6UzSdvncFJ6uYSaZC0ZYWISEx+h3zyO+Rz2W9hWOZs0SWSUbRIhYhIFcuXo4HNIg2UWnxERID5n8znzbVvMqbbuRQX9yW/uiUSRSStqfAREQHmrZrHrxf/mm1bcjj55L40bRp2RCKSDGnf1VVUBHff7f8VEUlU0XqfRHYtHk1OjnKKSEOV1i0+RUUwYgSUlMAxx8Crr8LgwWFHJSLpZn/Jft7b/B6N1g/hqdl9KS31uUU5RaThSesWn8JCX/SUlvp/CwvDjkhE0tGiDYsodaV03HYhhw4ZzimniDRUaV34nHWWb+nJyvL/nnVW2BGJSDpasH4BAF8fchBQThFpyNK6q2vwYN8UXVjoE5SapEUkEQs/WwjAWQM7Mr8VTJ8Ow4crp4g0RGld+IBPTEpOIlIfJ7Y8kW6tu9F420AGDoSbbw47IhFJlrTu6hIRCcIvz/klq69dzfYP87RwoUgDp8JHRCRm+XLo2zfsKEQkmVT4iEhGO1h6kG2fbwNg2TJtVSHS0KnwEZGMtn7Petr/vD1z3p3HunVw6qlhRyQiyaTCR0Qy2v6S/QBk78inVy/IyQk5IBFJKhU+IpLRviz9ktycXHb8s6fG94hkABU+IpLx+nXqx4r3sjS+RyQDqPARkYzXv1N/li3TjC6RTBB44WNmbczseTPbb2ZrzOziao4zM7vHzLbHPu4xMws6HhFJb6nIKacf158VK6BPn2BjF5HoScbKzQ8BJUBHoC/wZzNb7pxbWeW4KcB4oABwwCvAJ8BvkhCTiKSvpOeUdiX9ad8eWrUKNG4RiaBAW3zMLBeYANzinNvnnHsTeAm4NM7hlwP/5Zxb75z7DPgvYHKQ8YhIektFTunRtgc7P+pJv34BBi4ikRV0i09P4JBzrrjSc8uBYXGOzY99rfJx+fFe1Mym4O/mAA6a2fsBxJoM7YBtYQdRgyjHF+XYINrxRTk2gPqsjJOSnDLpkuz3/fP1iDQ5ov67jXJ8UY4Noh1flGOD+uWUwAuf5sCeKs/tBlpUc+zuKsc1NzNzzrnKBzrnZgGzAMxssXNuQHAhByfKsUG044tybBDt+KIcG/j46vHtyikRjQ2iHV+UY4Noxxfl2KDeOSXwwc37gJZVnmsJ7K3FsS2BfVUTlIhkNOUUEQlU0IVPMZBtZj0qPVcAVB2ESOy5glocJyKZSzlFRAIVaOHjnNsPPAfcYWa5ZjYEGAc8GefwJ4AfmdkJZnY8MA2YXYvTzAoq3iSIcmwQ7fiiHBtEO74oxwb1iE85JdKxQbTji3JsEO34ohwb1DM+C7oV2MzaAI8Bo4DtwI3OuafMbCjwf8655rHjDLgHuDL2rY8AN6hZWkQqU04RkSAFXviIiIiIRJW2rBAREZGMocJHREREMkbkCp+o7/VVh/huM7MvzWxfpY9uSY5tqpktNrODZjb7KMdeb2abzGyPmT1mZo2jEJuZTTaz0irX7awkx9bYzB6N/T73mtkyMzunhuNTdu3qElsY1y523jlmtjF2PYrN7Moajk3p313snMopicemnJJYbJHNKXWNL6Trl9yc4pyL1AcwF/gf/GJk38AvQpYf57gfAB8CJwInAKuAqyIU323AnBRfu/PxexU9DMyu4bjRwGb8qratgULgpxGJbTLwZoqvW27s99UVfzPwLfw6MV3DvnZ1jC3l1y523nygcezzPGAT0D/sa1fpvMopicemnJJYbJHNKQnEF8b1S2pOSdkPUodfRgnQs9JzT8b7QYC3gSmVHn8PWBCh+FKepCqd+86jJIKngLsqPR4BbIpIbCl/k1UTx3vAhChdu1rEFvq1wy8lvxG4IArXTjklsDiVU+ofZ2RzylHiC/X6JSOnRK2rq7p9eeLtt1PrfXkCVJf4AM41sx1mttLMrk5ybHUR79p1NLO2IcVT1elmti3WxHmLmQW9tUqNzKwj/ncdb/G7UK/dUWKDkK6dmf3azD4H/oFPUv8b57Awrp1ySmoop9QgyjkFoplXkplTolb4BLIvT5JiKz9nbeN7BugFtAe+D/zEzC5KYmx1Ee/aQfyfI9VeB74GdMDvyn0RMD1VJzezHOD3wO+cc/+Ic0ho164WsYV27ZxzP8Rfg6H4BQcPxjksjGunnJIayinViHJOgejmlWTmlKgVPlHfl6fW8TnnVjnnNjjnSp1zbwMPAN9OYmx1Ee/aQfzrnFLOuY+dc58458qccyuAO0jRdTOzRvhuhhJgajWHhXLtahNbmNcudv5SuzxySwAAA7RJREFU59yb+DEy8Vojwrh2yimpoZwSR5RzCkQ/ryQrp0St8In6vjx1ia8qByR9hkgtxbt2m51z20OKpyYpuW6xu/pHgY74fu4vqzk05deuDrFVFdbfXDZwSpznw/i7U05JDeWUKqKcU+oYX1Vh/N0Fm1PCGrBUw0Cmp/GzHHKBIVQ/w+Eq4AP87IvjYxcgFTMwahvfOPwocwMGAZ8Blyc5tmygCXA3vopvAmTHOW4MfpT8aUAr4DWSP4ugtrGdA3SMfZ4HvA/cmoLf62+ABUDzoxwXxrWrbWwpv3b45u+J+CbnLPwsi/3A2Chcu9h5lVMSj005JfH4IptT6hhfSq9fKnJKUi9sgj90G+CF2A+6Frg49vxQfLNz+XEG/AzYEfv4GbEtOCIS31z8vkL78IOzrk1BbLfhq/HKH7cBXWJxdKl07I/w0wD3AI8TmzoYdmzAvbG49gMf45tVc5Ic20mxeL6IxVL+cUnY164usYV07doDfwd2xa7HCuD7sa+F/ncXO6dySuKxKackFltkc0pd40v19UtFTtFeXSIiIpIxojbGR0RERCRpVPiIiIhIxlDhIyIiIhlDhY+IiIhkDBU+IiIikjFU+IiIiEjGUOEjIiIiGUOFj4iIiGQMFT4iIiKSMVT4SEqYWVMzW29ma82scZWvPWJmpWY2Maz4RCS9KKdIolT4SEo45w4AtwKdgR+WP29mdwPfA65xzj0dUngikmaUUyRR2qtLUsbMsoDl+N13uwFXAr/A7/R7R5ixiUj6UU6RRKjwkZQys28BfwReA4YDDzrnrg03KhFJV8opUlcqfCTlzOxd4HTgaeBiV+WP0MwuAK4F+gLbnHNdUx6kiKQN5RSpC43xkZQyswuBgtjDvVUTVMxO4EHgxykLTETSknKK1JVafCRlzOxsfJP0H4Evge8AvZ1zH1Rz/Hjgft2diUg8yimSCLX4SEqY2RnAc8BbwCXADKAMuDvMuEQkPSmnSKJU+EjSmdlpwP8CxcB459xB59xq4FFgnJkNCTVAEUkryilSHyp8JKnMrAvwV3wf+znOuT2VvjwTOAD8LIzYRCT9KKdIfWWHHYA0bM65tfgFxuJ9bQPQLLURiUg6U06R+lLhI5ETW5QsJ/ZhZtYEcM65g+FGJiLpSDlFKlPhI1F0KfB4pccHgDVA11CiEZF0p5wih2k6u4iIiGQMDW4WERGRjKHCR0RERDKGCh8RERHJGCp8REREJGOo8BEREZGMocJHREREMoYKHxEREckY/x/dtu6I9illMgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "np.random.seed(42)\n",
    "m = 20\n",
    "X = 3 * np.random.rand(m, 1)\n",
    "y = 1 + 0.5 * X + np.random.randn(m, 1) / 1.5\n",
    "X_new = np.linspace(0, 3, 100).reshape(100, 1)\n",
    "\n",
    "def plot_model(model_class, polynomial, alphas, **model_kargs):\n",
    "    for alpha, style in zip(alphas, (\"b-\", \"g--\", \"r:\")):\n",
    "        model = model_class(alpha, **model_kargs) if alpha > 0 else LinearRegression()\n",
    "        if polynomial:\n",
    "            model = Pipeline([\n",
    "                    (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
    "                    (\"std_scaler\", StandardScaler()),\n",
    "                    (\"regul_reg\", model),\n",
    "                ])\n",
    "        model.fit(X, y)\n",
    "        y_new_regul = model.predict(X_new)\n",
    "        lw = 2 if alpha > 0 else 1\n",
    "        plt.plot(X_new, y_new_regul, style, linewidth=lw, label=r\"$\\alpha = {}$\".format(alpha))\n",
    "    plt.plot(X, y, \"b.\", linewidth=3)\n",
    "    plt.legend(loc=\"upper left\", fontsize=15)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    plt.axis([0, 3, 0, 4])\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.subplot(121)\n",
    "plot_model(Ridge, polynomial=False, alphas=(0, 10, 100), random_state=42)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(122)\n",
    "plot_model(Ridge, polynomial=True, alphas=(0, 10**-5, 1), random_state=42)\n",
    "\n",
    "save_fig(\"ridge_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.55071465]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "ridge_reg = Ridge(alpha=1, solver=\"cholesky\", random_state=42)\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.49905184])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg = SGDRegressor(max_iter=50, tol=-np.infty, penalty=\"l2\", random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())\n",
    "sgd_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.5507201]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge_reg = Ridge(alpha=1, solver=\"sag\", random_state=42)\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure lasso_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.subplot(121)\n",
    "plot_model(Lasso, polynomial=False, alphas=(0, 0.1, 1), random_state=42)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(122)\n",
    "plot_model(Lasso, polynomial=True, alphas=(0, 10**-7, 1), tol=1, random_state=42)\n",
    "\n",
    "save_fig(\"lasso_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.53788174])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "lasso_reg = Lasso(alpha=0.1)\n",
    "lasso_reg.fit(X, y)\n",
    "lasso_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.54333232])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import ElasticNet\n",
    "elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5, random_state=42)\n",
    "elastic_net.fit(X, y)\n",
    "elastic_net.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure early_stopping_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 2 + X + 0.5 * X**2 + np.random.randn(m, 1)\n",
    "\n",
    "X_train, X_val, y_train, y_val = train_test_split(X[:50], y[:50].ravel(), test_size=0.5, random_state=10)\n",
    "\n",
    "poly_scaler = Pipeline([\n",
    "        (\"poly_features\", PolynomialFeatures(degree=90, include_bias=False)),\n",
    "        (\"std_scaler\", StandardScaler()),\n",
    "    ])\n",
    "\n",
    "X_train_poly_scaled = poly_scaler.fit_transform(X_train)\n",
    "X_val_poly_scaled = poly_scaler.transform(X_val)\n",
    "\n",
    "sgd_reg = SGDRegressor(max_iter=1,\n",
    "                       tol=-np.infty,\n",
    "                       penalty=None,\n",
    "                       eta0=0.0005,\n",
    "                       warm_start=True,\n",
    "                       learning_rate=\"constant\",\n",
    "                       random_state=42)\n",
    "\n",
    "n_epochs = 500\n",
    "train_errors, val_errors = [], []\n",
    "for epoch in range(n_epochs):\n",
    "    sgd_reg.fit(X_train_poly_scaled, y_train)\n",
    "    y_train_predict = sgd_reg.predict(X_train_poly_scaled)\n",
    "    y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
    "    train_errors.append(mean_squared_error(y_train, y_train_predict))\n",
    "    val_errors.append(mean_squared_error(y_val, y_val_predict))\n",
    "\n",
    "best_epoch = np.argmin(val_errors)\n",
    "best_val_rmse = np.sqrt(val_errors[best_epoch])\n",
    "\n",
    "plt.annotate('Best model',\n",
    "             xy=(best_epoch, best_val_rmse),\n",
    "             xytext=(best_epoch, best_val_rmse + 1),\n",
    "             ha=\"center\",\n",
    "             arrowprops=dict(facecolor='black', shrink=0.05),\n",
    "             fontsize=16,\n",
    "            )\n",
    "\n",
    "best_val_rmse -= 0.03  # just to make the graph look better\n",
    "plt.plot([0, n_epochs], [best_val_rmse, best_val_rmse], \"k:\", linewidth=2)\n",
    "plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"Validation set\")\n",
    "plt.plot(np.sqrt(train_errors), \"r--\", linewidth=2, label=\"Training set\")\n",
    "plt.legend(loc=\"upper right\", fontsize=14)\n",
    "plt.xlabel(\"Epoch\", fontsize=14)\n",
    "plt.ylabel(\"RMSE\", fontsize=14)\n",
    "save_fig(\"early_stopping_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.base import clone\n",
    "sgd_reg = SGDRegressor(max_iter=1, tol=-np.infty, warm_start=True, penalty=None,\n",
    "                       learning_rate=\"constant\", eta0=0.0005, random_state=42)\n",
    "\n",
    "minimum_val_error = float(\"inf\")\n",
    "best_epoch = None\n",
    "best_model = None\n",
    "for epoch in range(1000):\n",
    "    sgd_reg.fit(X_train_poly_scaled, y_train)  # continues where it left off\n",
    "    y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
    "    val_error = mean_squared_error(y_val, y_val_predict)\n",
    "    if val_error < minimum_val_error:\n",
    "        minimum_val_error = val_error\n",
    "        best_epoch = epoch\n",
    "        best_model = clone(sgd_reg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(239,\n",
       " SGDRegressor(alpha=0.0001, average=False, early_stopping=False, epsilon=0.1,\n",
       "        eta0=0.0005, fit_intercept=True, l1_ratio=0.15,\n",
       "        learning_rate='constant', loss='squared_loss', max_iter=1,\n",
       "        n_iter=None, n_iter_no_change=5, penalty=None, power_t=0.25,\n",
       "        random_state=42, shuffle=True, tol=-inf, validation_fraction=0.1,\n",
       "        verbose=0, warm_start=True))"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_epoch, best_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "t1a, t1b, t2a, t2b = -1, 3, -1.5, 1.5\n",
    "\n",
    "# ignoring bias term\n",
    "t1s = np.linspace(t1a, t1b, 500)\n",
    "t2s = np.linspace(t2a, t2b, 500)\n",
    "t1, t2 = np.meshgrid(t1s, t2s)\n",
    "T = np.c_[t1.ravel(), t2.ravel()]\n",
    "Xr = np.array([[-1, 1], [-0.3, -1], [1, 0.1]])\n",
    "yr = 2 * Xr[:, :1] + 0.5 * Xr[:, 1:]\n",
    "\n",
    "J = (1/len(Xr) * np.sum((T.dot(Xr.T) - yr.T)**2, axis=1)).reshape(t1.shape)\n",
    "\n",
    "N1 = np.linalg.norm(T, ord=1, axis=1).reshape(t1.shape)\n",
    "N2 = np.linalg.norm(T, ord=2, axis=1).reshape(t1.shape)\n",
    "\n",
    "t_min_idx = np.unravel_index(np.argmin(J), J.shape)\n",
    "t1_min, t2_min = t1[t_min_idx], t2[t_min_idx]\n",
    "\n",
    "t_init = np.array([[0.25], [-1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure lasso_vs_ridge_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def bgd_path(theta, X, y, l1, l2, core = 1, eta = 0.1, n_iterations = 50):\n",
    "    path = [theta]\n",
    "    for iteration in range(n_iterations):\n",
    "        gradients = core * 2/len(X) * X.T.dot(X.dot(theta) - y) + l1 * np.sign(theta) + 2 * l2 * theta\n",
    "\n",
    "        theta = theta - eta * gradients\n",
    "        path.append(theta)\n",
    "    return np.array(path)\n",
    "\n",
    "plt.figure(figsize=(12, 8))\n",
    "for i, N, l1, l2, title in ((0, N1, 0.5, 0, \"Lasso\"), (1, N2, 0,  0.1, \"Ridge\")):\n",
    "    JR = J + l1 * N1 + l2 * N2**2\n",
    "    \n",
    "    tr_min_idx = np.unravel_index(np.argmin(JR), JR.shape)\n",
    "    t1r_min, t2r_min = t1[tr_min_idx], t2[tr_min_idx]\n",
    "\n",
    "    levelsJ=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(J) - np.min(J)) + np.min(J)\n",
    "    levelsJR=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(JR) - np.min(JR)) + np.min(JR)\n",
    "    levelsN=np.linspace(0, np.max(N), 10)\n",
    "    \n",
    "    path_J = bgd_path(t_init, Xr, yr, l1=0, l2=0)\n",
    "    path_JR = bgd_path(t_init, Xr, yr, l1, l2)\n",
    "    path_N = bgd_path(t_init, Xr, yr, np.sign(l1)/3, np.sign(l2), core=0)\n",
    "\n",
    "    plt.subplot(221 + i * 2)\n",
    "    plt.grid(True)\n",
    "    plt.axhline(y=0, color='k')\n",
    "    plt.axvline(x=0, color='k')\n",
    "    plt.contourf(t1, t2, J, levels=levelsJ, alpha=0.9)\n",
    "    plt.contour(t1, t2, N, levels=levelsN)\n",
    "    plt.plot(path_J[:, 0], path_J[:, 1], \"w-o\")\n",
    "    plt.plot(path_N[:, 0], path_N[:, 1], \"y-^\")\n",
    "    plt.plot(t1_min, t2_min, \"rs\")\n",
    "    plt.title(r\"$\\ell_{}$ penalty\".format(i + 1), fontsize=16)\n",
    "    plt.axis([t1a, t1b, t2a, t2b])\n",
    "    if i == 1:\n",
    "        plt.xlabel(r\"$\\theta_1$\", fontsize=20)\n",
    "    plt.ylabel(r\"$\\theta_2$\", fontsize=20, rotation=0)\n",
    "\n",
    "    plt.subplot(222 + i * 2)\n",
    "    plt.grid(True)\n",
    "    plt.axhline(y=0, color='k')\n",
    "    plt.axvline(x=0, color='k')\n",
    "    plt.contourf(t1, t2, JR, levels=levelsJR, alpha=0.9)\n",
    "    plt.plot(path_JR[:, 0], path_JR[:, 1], \"w-o\")\n",
    "    plt.plot(t1r_min, t2r_min, \"rs\")\n",
    "    plt.title(title, fontsize=16)\n",
    "    plt.axis([t1a, t1b, t2a, t2b])\n",
    "    if i == 1:\n",
    "        plt.xlabel(r\"$\\theta_1$\", fontsize=20)\n",
    "\n",
    "save_fig(\"lasso_vs_ridge_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_function_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(-10, 10, 100)\n",
    "sig = 1 / (1 + np.exp(-t))\n",
    "plt.figure(figsize=(9, 3))\n",
    "plt.plot([-10, 10], [0, 0], \"k-\")\n",
    "plt.plot([-10, 10], [0.5, 0.5], \"k:\")\n",
    "plt.plot([-10, 10], [1, 1], \"k:\")\n",
    "plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n",
    "plt.plot(t, sig, \"b-\", linewidth=2, label=r\"$\\sigma(t) = \\frac{1}{1 + e^{-t}}$\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.legend(loc=\"upper left\", fontsize=20)\n",
    "plt.axis([-10, 10, -0.1, 1.1])\n",
    "save_fig(\"logistic_function_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['data', 'target', 'target_names', 'DESCR', 'feature_names', 'filename']"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "iris = datasets.load_iris()\n",
    "list(iris.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _iris_dataset:\n",
      "\n",
      "Iris plants dataset\n",
      "--------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 150 (50 in each of three classes)\n",
      "    :Number of Attributes: 4 numeric, predictive attributes and the class\n",
      "    :Attribute Information:\n",
      "        - sepal length in cm\n",
      "        - sepal width in cm\n",
      "        - petal length in cm\n",
      "        - petal width in cm\n",
      "        - class:\n",
      "                - Iris-Setosa\n",
      "                - Iris-Versicolour\n",
      "                - Iris-Virginica\n",
      "                \n",
      "    :Summary Statistics:\n",
      "\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "                    Min  Max   Mean    SD   Class Correlation\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "    sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
      "    sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
      "    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
      "    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "    :Class Distribution: 33.3% for each of 3 classes.\n",
      "    :Creator: R.A. Fisher\n",
      "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      "    :Date: July, 1988\n",
      "\n",
      "The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\n",
      "from Fisher's paper. Note that it's the same as in R, but not as in the UCI\n",
      "Machine Learning Repository, which has two wrong data points.\n",
      "\n",
      "This is perhaps the best known database to be found in the\n",
      "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
      "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
      "data set contains 3 classes of 50 instances each, where each class refers to a\n",
      "type of iris plant.  One class is linearly separable from the other 2; the\n",
      "latter are NOT linearly separable from each other.\n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "   - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\n",
      "     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
      "     Mathematical Statistics\" (John Wiley, NY, 1950).\n",
      "   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\n",
      "     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
      "   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
      "     Structure and Classification Rule for Recognition in Partially Exposed\n",
      "     Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
      "     Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
      "   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
      "     on Information Theory, May 1972, 431-433.\n",
      "   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
      "     conceptual clustering system finds 3 classes in the data.\n",
      "   - Many, many more ...\n"
     ]
    }
   ],
   "source": [
    "print(iris.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris[\"data\"][:, 3:]  # petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int)  # 1 if Iris-Virginica, else 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='warn',\n",
       "          n_jobs=None, penalty='l2', random_state=42, solver='liblinear',\n",
       "          tol=0.0001, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "log_reg = LogisticRegression(solver=\"liblinear\", random_state=42)\n",
    "log_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10bfe7cf8>]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris-Virginica\")\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris-Virginica\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure in the book actually is actually a bit fancier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "decision_boundary = X_new[y_proba[:, 1] >= 0.5][0]\n",
    "\n",
    "plt.figure(figsize=(8, 3))\n",
    "plt.plot(X[y==0], y[y==0], \"bs\")\n",
    "plt.plot(X[y==1], y[y==1], \"g^\")\n",
    "plt.plot([decision_boundary, decision_boundary], [-1, 2], \"k:\", linewidth=2)\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris-Virginica\")\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris-Virginica\")\n",
    "plt.text(decision_boundary+0.02, 0.15, \"Decision  boundary\", fontsize=14, color=\"k\", ha=\"center\")\n",
    "plt.arrow(decision_boundary, 0.08, -0.3, 0, head_width=0.05, head_length=0.1, fc='b', ec='b')\n",
    "plt.arrow(decision_boundary, 0.92, 0.3, 0, head_width=0.05, head_length=0.1, fc='g', ec='g')\n",
    "plt.xlabel(\"Petal width (cm)\", fontsize=14)\n",
    "plt.ylabel(\"Probability\", fontsize=14)\n",
    "plt.legend(loc=\"center left\", fontsize=14)\n",
    "plt.axis([0, 3, -0.02, 1.02])\n",
    "save_fig(\"logistic_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.61561562])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decision_boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.predict([[1.7], [1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_regression_contour_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int)\n",
    "\n",
    "log_reg = LogisticRegression(solver=\"liblinear\", C=10**10, random_state=42)\n",
    "log_reg.fit(X, y)\n",
    "\n",
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(2.9, 7, 500).reshape(-1, 1),\n",
    "        np.linspace(0.8, 2.7, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"bs\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"g^\")\n",
    "\n",
    "zz = y_proba[:, 1].reshape(x0.shape)\n",
    "contour = plt.contour(x0, x1, zz, cmap=plt.cm.brg)\n",
    "\n",
    "\n",
    "left_right = np.array([2.9, 7])\n",
    "boundary = -(log_reg.coef_[0][0] * left_right + log_reg.intercept_[0]) / log_reg.coef_[0][1]\n",
    "\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.plot(left_right, boundary, \"k--\", linewidth=3)\n",
    "plt.text(3.5, 1.5, \"Not Iris-Virginica\", fontsize=14, color=\"b\", ha=\"center\")\n",
    "plt.text(6.5, 2.3, \"Iris-Virginica\", fontsize=14, color=\"g\", ha=\"center\")\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.axis([2.9, 7, 0.8, 2.7])\n",
    "save_fig(\"logistic_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=10, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='multinomial',\n",
       "          n_jobs=None, penalty='l2', random_state=42, solver='lbfgs',\n",
       "          tol=0.0001, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = iris[\"target\"]\n",
    "\n",
    "softmax_reg = LogisticRegression(multi_class=\"multinomial\",solver=\"lbfgs\", C=10, random_state=42)\n",
    "softmax_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure softmax_regression_contour_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(0, 8, 500).reshape(-1, 1),\n",
    "        np.linspace(0, 3.5, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "\n",
    "y_proba = softmax_reg.predict_proba(X_new)\n",
    "y_predict = softmax_reg.predict(X_new)\n",
    "\n",
    "zz1 = y_proba[:, 1].reshape(x0.shape)\n",
    "zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==2, 0], X[y==2, 1], \"g^\", label=\"Iris-Virginica\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"bs\", label=\"Iris-Versicolor\")\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"yo\", label=\"Iris-Setosa\")\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "\n",
    "plt.contourf(x0, x1, zz, cmap=custom_cmap)\n",
    "contour = plt.contour(x0, x1, zz1, cmap=plt.cm.brg)\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.legend(loc=\"center left\", fontsize=14)\n",
    "plt.axis([0, 7, 0, 3.5])\n",
    "save_fig(\"softmax_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict([[5, 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6.38014896e-07, 5.74929995e-02, 9.42506362e-01]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict_proba([[5, 2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. to 11."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See appendix A."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12. Batch Gradient Descent with early stopping for Softmax Regression\n",
    "(without using Scikit-Learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start by loading the data. We will just reuse the Iris dataset we loaded earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = iris[\"target\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to add the bias term for every instance ($x_0 = 1$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_with_bias = np.c_[np.ones([len(X), 1]), X]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And let's set the random seed so the output of this exercise solution is reproducible:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(2042)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The easiest option to split the dataset into a training set, a validation set and a test set would be to use Scikit-Learn's `train_test_split()` function, but the point of this exercise is to try understand the algorithms by implementing them manually. So here is one possible implementation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_ratio = 0.2\n",
    "validation_ratio = 0.2\n",
    "total_size = len(X_with_bias)\n",
    "\n",
    "test_size = int(total_size * test_ratio)\n",
    "validation_size = int(total_size * validation_ratio)\n",
    "train_size = total_size - test_size - validation_size\n",
    "\n",
    "rnd_indices = np.random.permutation(total_size)\n",
    "\n",
    "X_train = X_with_bias[rnd_indices[:train_size]]\n",
    "y_train = y[rnd_indices[:train_size]]\n",
    "X_valid = X_with_bias[rnd_indices[train_size:-test_size]]\n",
    "y_valid = y[rnd_indices[train_size:-test_size]]\n",
    "X_test = X_with_bias[rnd_indices[-test_size:]]\n",
    "y_test = y[rnd_indices[-test_size:]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The targets are currently class indices (0, 1 or 2), but we need target class probabilities to train the Softmax Regression model. Each instance will have target class probabilities equal to 0.0 for all classes except for the target class which will have a probability of 1.0 (in other words, the vector of class probabilities for ay given instance is a one-hot vector). Let's write a small function to convert the vector of class indices into a matrix containing a one-hot vector for each instance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "def to_one_hot(y):\n",
    "    n_classes = y.max() + 1\n",
    "    m = len(y)\n",
    "    Y_one_hot = np.zeros((m, n_classes))\n",
    "    Y_one_hot[np.arange(m), y] = 1\n",
    "    return Y_one_hot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's test this function on the first 10 instances:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 1, 1, 0, 1, 1, 1, 0])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [1., 0., 0.]])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "to_one_hot(y_train[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks good, so let's create the target class probabilities matrix for the training set and the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_train_one_hot = to_one_hot(y_train)\n",
    "Y_valid_one_hot = to_one_hot(y_valid)\n",
    "Y_test_one_hot = to_one_hot(y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's implement the Softmax function. Recall that it is defined by the following equation:\n",
    "\n",
    "$\\sigma\\left(\\mathbf{s}(\\mathbf{x})\\right)_k = \\dfrac{\\exp\\left(s_k(\\mathbf{x})\\right)}{\\sum\\limits_{j=1}^{K}{\\exp\\left(s_j(\\mathbf{x})\\right)}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "def softmax(logits):\n",
    "    exps = np.exp(logits)\n",
    "    exp_sums = np.sum(exps, axis=1, keepdims=True)\n",
    "    return exps / exp_sums"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are almost ready to start training. Let's define the number of inputs and outputs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_inputs = X_train.shape[1] # == 3 (2 features plus the bias term)\n",
    "n_outputs = len(np.unique(y_train))   # == 3 (3 iris classes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now here comes the hardest part: training! Theoretically, it's simple: it's just a matter of translating the math equations into Python code. But in practice, it can be quite tricky: in particular, it's easy to mix up the order of the terms, or the indices. You can even end up with code that looks like it's working but is actually not computing exactly the right thing. When unsure, you should write down the shape of each term in the equation and make sure the corresponding terms in your code match closely. It can also help to evaluate each term independently and print them out. The good news it that you won't have to do this everyday, since all this is well implemented by Scikit-Learn, but it will help you understand what's going on under the hood.\n",
    "\n",
    "So the equations we will need are the cost function:\n",
    "\n",
    "$J(\\mathbf{\\Theta}) =\n",
    "- \\dfrac{1}{m}\\sum\\limits_{i=1}^{m}\\sum\\limits_{k=1}^{K}{y_k^{(i)}\\log\\left(\\hat{p}_k^{(i)}\\right)}$\n",
    "\n",
    "And the equation for the gradients:\n",
    "\n",
    "$\\nabla_{\\mathbf{\\theta}^{(k)}} \\, J(\\mathbf{\\Theta}) = \\dfrac{1}{m} \\sum\\limits_{i=1}^{m}{ \\left ( \\hat{p}^{(i)}_k - y_k^{(i)} \\right ) \\mathbf{x}^{(i)}}$\n",
    "\n",
    "Note that $\\log\\left(\\hat{p}_k^{(i)}\\right)$ may not be computable if $\\hat{p}_k^{(i)} = 0$. So we will add a tiny value $\\epsilon$ to $\\log\\left(\\hat{p}_k^{(i)}\\right)$ to avoid getting `nan` values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 5.446205811872683\n",
      "500 0.8350062641405651\n",
      "1000 0.6878801447192402\n",
      "1500 0.6012379137693314\n",
      "2000 0.5444496861981872\n",
      "2500 0.5038530181431525\n",
      "3000 0.47292289721922487\n",
      "3500 0.44824244188957774\n",
      "4000 0.4278651093928793\n",
      "4500 0.41060071429187134\n",
      "5000 0.3956780375390374\n"
     ]
    }
   ],
   "source": [
    "eta = 0.01\n",
    "n_iterations = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-7\n",
    "\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    logits = X_train.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    if iteration % 500 == 0:\n",
    "        print(iteration, loss)\n",
    "    gradients = 1/m * X_train.T.dot(error)\n",
    "    Theta = Theta - eta * gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And that's it! The Softmax model is trained. Let's look at the model parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.32094157, -0.6501102 , -2.99979416],\n",
       "       [-1.1718465 ,  0.11706172,  0.10507543],\n",
       "       [-0.70224261, -0.09527802,  1.4786383 ]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make predictions for the validation set and check the accuracy score:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9666666666666667"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_valid)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, this model looks pretty good. For the sake of the exercise, let's add a bit of $\\ell_2$ regularization. The following training code is similar to the one above, but the loss now has an additional $\\ell_2$ penalty, and the gradients have the proper additional term (note that we don't regularize the first element of `Theta` since this corresponds to the bias term). Also, let's try increasing the learning rate `eta`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 6.629842469083912\n",
      "500 0.5339667976629505\n",
      "1000 0.5036400750148942\n",
      "1500 0.49468910594603216\n",
      "2000 0.4912968418075476\n",
      "2500 0.48989924700933296\n",
      "3000 0.4892990598451198\n",
      "3500 0.4890351244397859\n",
      "4000 0.4889173621830818\n",
      "4500 0.4888643337449303\n",
      "5000 0.4888403120738818\n"
     ]
    }
   ],
   "source": [
    "eta = 0.1\n",
    "n_iterations = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-7\n",
    "alpha = 0.1  # regularization hyperparameter\n",
    "\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    logits = X_train.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    xentropy_loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n",
    "    loss = xentropy_loss + alpha * l2_loss\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    if iteration % 500 == 0:\n",
    "        print(iteration, loss)\n",
    "    gradients = 1/m * X_train.T.dot(error) + np.r_[np.zeros([1, n_outputs]), alpha * Theta[1:]]\n",
    "    Theta = Theta - eta * gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because of the additional $\\ell_2$ penalty, the loss seems greater than earlier, but perhaps this model will perform better? Let's find out:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_valid)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cool, perfect accuracy! We probably just got lucky with this validation set, but still, it's pleasant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's add early stopping. For this we just need to measure the loss on the validation set at every iteration and stop when the error starts growing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 4.7096017363419875\n",
      "500 0.5739711987633519\n",
      "1000 0.5435638529109128\n",
      "1500 0.5355752782580262\n",
      "2000 0.5331959249285545\n",
      "2500 0.5325946767399382\n",
      "2765 0.5325460966791898\n",
      "2766 0.5325460971327978 early stopping!\n"
     ]
    }
   ],
   "source": [
    "eta = 0.1 \n",
    "n_iterations = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-7\n",
    "alpha = 0.1  # regularization hyperparameter\n",
    "best_loss = np.infty\n",
    "\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    logits = X_train.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    xentropy_loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n",
    "    loss = xentropy_loss + alpha * l2_loss\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    gradients = 1/m * X_train.T.dot(error) + np.r_[np.zeros([1, n_outputs]), alpha * Theta[1:]]\n",
    "    Theta = Theta - eta * gradients\n",
    "\n",
    "    logits = X_valid.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    xentropy_loss = -np.mean(np.sum(Y_valid_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n",
    "    loss = xentropy_loss + alpha * l2_loss\n",
    "    if iteration % 500 == 0:\n",
    "        print(iteration, loss)\n",
    "    if loss < best_loss:\n",
    "        best_loss = loss\n",
    "    else:\n",
    "        print(iteration - 1, best_loss)\n",
    "        print(iteration, loss, \"early stopping!\")\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_valid)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Still perfect, but faster."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's plot the model's predictions on the whole dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(0, 8, 500).reshape(-1, 1),\n",
    "        np.linspace(0, 3.5, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "X_new_with_bias = np.c_[np.ones([len(X_new), 1]), X_new]\n",
    "\n",
    "logits = X_new_with_bias.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "zz1 = Y_proba[:, 1].reshape(x0.shape)\n",
    "zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==2, 0], X[y==2, 1], \"g^\", label=\"Iris-Virginica\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"bs\", label=\"Iris-Versicolor\")\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"yo\", label=\"Iris-Setosa\")\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "\n",
    "plt.contourf(x0, x1, zz, cmap=custom_cmap)\n",
    "contour = plt.contour(x0, x1, zz1, cmap=plt.cm.brg)\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([0, 7, 0, 3.5])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now let's measure the final model's accuracy on the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9333333333333333"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_test.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_test)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our perfect model turns out to have slight imperfections. This variability is likely due to the very small size of the dataset: depending on how you sample the training set, validation set and the test set, you can get quite different results. Try changing the random seed and running the code again a few times, you will see that the results will vary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  },
  "nav_menu": {},
  "toc": {
   "navigate_menu": true,
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